Abstract <p> The paper considers the transverse vibrations of two strings connected to each other at acertain point. A mathematical model of this process, based on the law of conservation ofmomentum, expressed in the form of an integro-differential equation is constructed. This equationconnects the deviations of the strings during vibrations with their characteristics such as density,tension, and sources of external forces. This approach can be considered as a development of themethod proposed by A.N. Tikhonov for the equation of string vibrations with nonsmooth data.For the case where the densities of the strings are constants, we set a nonclassical problem for theintegro-differential equation. In addition to the Cauchy data, the problem includes necessarymatching conditions. A theorem on the existence and uniqueness of a solution to the problem isproved, and explicit formulas are obtained for its solution.</p>