The defendant was tried before a jury in the Superior Court and found guilty of murder in the first degree, G. L. c. 265, § 1 (1986 ed.), and of breaking and entering a dwelling house in the nighttime with the intent to commit a felony and committing an assault on a person lawfully therein, G. L. c. 266, § 14 (1986 ed.). On appeal, the defendant contends that the judge erred in admitting testimony of witnesses to the victim’s hearsay statements accusing the defendant of having committed prior crimes and. of violently attacking the victim.
We summarize the facts as they may have appeared to the jury. In 1984, the defendant and his girlfriend, the victim, moved from Brooklyn, New York, to the Dorchester area of Boston. In early February, 1985, the victim’s cousin Joyce, and Joyce’s four year old son came to visit the victim. During the next week, the defendant and the victim were “constantly *137arguing.” On February 13, 1985, the victim went with Joyce and Joyce’s son to the Malden apartment of Cynthia, a friend of the victim. There, the victim told Cynthia that the defendant had done “something to somebody in New York”; that he had beaten up the victim; and that she feared for her life and wanted to go to the police and have the defendant arrested. Cynthia directed the victim to the police station, where the victim told a police officer, Sergeant Richard Cox, that the defendant had stabbed and killed a woman in Brooklyn, New York. She also told Cox that the defendant had beaten her, and that she wanted him removed from the apartment they shared. Sergeant Cox told the victim to stay at a friend’s house for the night, and that he would check out her story with the Brooklyn police and get back to her in the morning. The victim then returned to Cynthia’s apartment to spend the night.
That night, the victim, Joyce, and Joyce’s son stayed in the front room of Cynthia’s apartment. All three slept in the same bed to keep warm. Cynthia and her boyfriend, Quintín, were in the back bedroom. At some point, Joyce awakened to see a man lying flat on the floor near the bed. There was evidence introduced from which the jury could have found that this intruder broke and entered through the back door of the apartment. Joyce roused the victim, and the two of them sat up in the bed. The man on the floor got up, began hitting the victim, and pulled her off the bed onto the floor. When Joyce got off the bed to try to help the victim, she recognized the man as the defendant and saw that he had a knife. The defendant raised the knife and repeatedly stabbed the victim as she lay on the floor. He told Joyce to lie down and shut up or he would do the same to her. The defendant then took the victim’s coat and covered her body, kissed her forehead, and said, “I killed Nivea for you and now I’m killing you for Nivea.”1 Cynthia and Quintín entered the room, and the defendant said, “The bitch called the police on me. She’s no good. She called the police.” The defendant then put the knife into the waistband of *138his pants, and went into the bathroom to wash the bloodstains off his clothes. To get the defendant out of the apartment, Quintín gave him some money for a taxi. At this point, it was about 4 a.m. The defendant asked Quintín to give him until 6 a.m. “to get away.” When the defendant left the apartment, Quintín and Cynthia went to the Malden police station.
The defendant was apprehended at the apartment of a coworker. Daniel Stamos, the defendant’s employer, identified the defendant for the police, and asked the defendant what had happened. The defendant started crying and responded, “I’m sorry, Mr. Danny, I killed my wife. I killed my baby.” The police found near the defendant items of clothing which he admitted he had been wearing on the night the victim was killed; on these were found traces of blood of the same type as the victim’s.
At trial the defendant denied having killed the victim, and testified that he had arrived at the scene of the crime to find the victim lying on the floor in a pool of blood. On appeal, the defendant contends that he was prejudiced substantially by the judge’s erroneous admission of testimony as to certain statements by the victim. Joyce, Cynthia, and Sergeant Cox testified to statements by the victim accusing the defendant of having stabbed and killed a woman in New York. Joyce and Cynthia also testified that the victim had stated that the defendant had beaten her. This testimony ostensibly was admitted for the nonhearsay purposes of showing a hostile relationship between the defendant and the victim, and the defendant’s motive for killing the victim. The defendant argues that the statements were hearsay, that their probative value was substantially outweighed by their prejudicial effect, and that the limiting instructions2 given were ineffective to prevent the jury from improperly considering the statements for the truth of the matters asserted.
*139Assuming arguendo, without deciding, that the judge erred in admitting in evidence the victim’s statements accusing the defendant of having beaten her and of having murdered another woman, we decline to reverse the defendant’s convictions because we conclude that the evidence properly admitted against the defendant was so overwhelming that no prejudice to the defendant actually resulted from the admission of the victim’s statements.
The evidence against the defendant was cumulative and compelling. Joyce testified that she saw the defendant beat and stab the victim, and then kneel over the victim’s body and say, “I killed Nivea for you and now I’m killing you for Nivea.” Cynthia also heard this statement. During the assault, the defendant told Joyce to lie down and shut up, or he would do the same to her. Quintín saw the defendant standing over the victim’s body holding a hunting knife, and both Quintín and Cynthia heard the defendant say, “The bitch called the police on me. She’s no good. She called the police.” On leaving Cynthia’s apartment, the defendant asked Quintín to give him some time “to get away.” Moreover, three disinterested witnesses testified regarding damaging admissions by the defendant. Two police officers testified that on his arrest the defendant said, “You have got the right guy. I killed her.” One of the officers asked the defendant where the murder weapon was, and the defendant told him it was still in Cynthia’s apartment. When the defendant’s employer, Daniel Stamos, who was present at the defendant’s arrest, asked him what had happened, the defendant replied, “I’m sorry, Mr. Danny. I killed my wife. I killed my baby.” Even if the jury had had doubts as to the credibility of Joyce, Cynthia, and Quintín, it reasonably could have relied on the testimony of Stamos and the police officers. Although not inconsistent with the defendant’s version of the facts, the traces of blood of the victim’s type that were found on the defendant’s clothing provide additional circumstantial evidence of guilt.
This, then, is that rare case in which the evidence properly admitted against the defendant is so overwhelming that there is no reasonable possibility that the exclusion of the evidence *140complained of would have affected the jury’s verdict. Even if the victim’s statements had been excluded, “we can say with fair assurance that a reasonable jury would not have returned a different verdict.” Commonwealth v. Helfant, 398 Mass. 214, 223 (1986). We also have reviewed the entire record as required by G. L. c. 278, § 33E (1986 ed.), and decline to order a new trial or to direct the entry of a verdict of a lesser degree of guilt.
Judgments affirmed.
The defendant testified that he knew a woman named “Nivea” in Brooklyn, New York, and that Nivea was the mother of his child.
The judge instructed the jury that the statements were hearsay; that they were not admitted to prove the truth of the matters asserted or to show that the defendant committed or had a propensity to commit the crimes charged; and that the jury should consider them only for the limited purposes of proving the victim’s state of mind and the defendant’s knowledge, intent, motive, or method.