Аннотация:We study a new class of time-periodic solutions of singularly perturbed systems ofreaction–diffusion equations in the case of a fast and a slow equation, which are usually called Tikhonov-type systems. A boundary layer asymptotics of solutions is constructed, the existence of solutions with this asymptotics is proved, and conditions for the Lyapunov asymptotic stability of these solutions treated as solutions of the corresponding initial–boudary value problems areobtained.