Order unanimously affirmed with costs. Memorandum: Special Term properly denied respondent’s application to stay arbitration. Claimants contend that distinct injuries and damages were sustained as a result of two successive automobile collisions. Since the driver of the second automobile that collided with theirs was uninsured, claimants are entitled to arbitration under the uninsured motorist indorsement of respondent’s policy of insurance issued to claimant Royal Johnson Sovie. Claimants seek only to arbitrate their claims for injuries and *996damages sustained in the collision with the uninsured vehicle. They do not seek to "stack” the uninsured motorist coverage and the amount received by jury verdict against the insured driver whose vehicle was the first to collide with theirs (cf., Matter of Nationwide Mut. Ins. Co. [Miller], 111 AD2d 438, lv dismissed 66 NY2d 604, 915; Sisson v Travelers Ins. Cos., 94 AD2d 953; State Farm Mut. Auto. Ins. Co. v Basile, 48 AD2d 868). Accordingly, the court properly found that, since the necessary preconditions had been met, arbitration should proceed (see, Matter of Aetna Cas. & Sur. Co. v Cochrane, 64 NY2d 796). (Appeal from order of Supreme Court, Onondaga County, Tenney, J. — arbitration.) Present — Dillon, P. J., Callahan, Denman, Pine and Lawton, JJ.