Аннотация:The paper is devoted to the partial stability problem for the system x ˙=X(t,x,μ), x∈ℝ n with respect to the variables x 1 ,⋯,x m (m<n) under a small parameter μ≥0. The authors introduce the notions of partial μ-stability and asymptotic partial μ-stability for this system. The μ-stability means that for sufficiently small μ all system trajectories which are close to the origin at the moment t=t 0 remain so for all t>t 0 . The unperturbed system x ˙=X(t,x,0) is assumed to be nonasymptotically stable. The main result consists in obtaining new sufficient conditions for partial μ-stability of the original system. Those are given in terms of positive definiteness of a Lyapunov-type auxiliary function v(t,x) with respect to x 1 ,⋯,x m . A couple of example are considered for third-order dynamic systems.