In this note we consider the almost sure convergence (as ϵ→0) of solution Xϵ(·), defined over the interval 0 ≤ τ ≤ 1, of the random ordinary differential equation View the MathML source Here {F(x, t, ω), t ≥ 0} is a strong mixing process for each x and (x, t) → F(x, t, ω) is subject to regularity conditions which ensure the existence of a unique solution over 0 ≤ τ ≤ 1 for all ϵ > 0. Under rather weak conditions it is shown that the function Xϵ(·, ω) converges a.s. to the solution x0(·) of a non-random averaged differential equation View the MathML source the convergence being uniform over 0 ≤ τ ≤ 1.