Suppose that ℝ n is the p-dimensional space with Euclidean norm ∥ ⋅ ∥, K (ℝ p ) is the set of nonempty compact sets in ℝ p , ℝ+ = [0, +∞), D = ℝ+ × ℝ m × ℝ n × [0, a], D0 = ℝ+ × ℝ m , F0: D0 → K (ℝ m ), and co F0 is the convex cover of the mapping F0. We consider the Cauchy problem for the system of differential inclusions $$\dot x \in \mu F(t,x,y,\mu ),\quad \dot y \in G(t,x,y,\mu ),\quad x(0) = x_0 ,\quad y(0) = y_0$$ with slow x and fast y variables; here F: D → K (ℝ m ), G: D → K (ℝ n ), and μ ∈ [0, a] is a small parameter. It is assumed that this problem has at least one solution on [0, 1/μ] for all sufficiently small μ ∈ [0, a]. Under certain conditions on F, G, and F0, comprising both the usual conditions for approximation problems and some new ones (which are weaker than the Lipschitz property), it is proved that, for any e > 0, there is a μ0 > 0 such that for any μ ∈ (0, μ0] and any solution (xμ(t), yμ(t)) of the problem under consideration, there exists a solution uμ(t) of the problem \({\dot u}\) ∈ μ co F0 (t, u), u(0) = x0 for which the inequality ∥xμ(t) − uμ(t)∥ < e holds for each t ∈ [0, 1/μ].