In this paper, we study the asymptotic behavior of linear differential equations under nonlinear perturbation. Let’s consider the delay differential equations: dx = Ax + f(t, xt ), dt where t ∈ R+ , A ∈ L(E), f : R+ × E −→ E and (T (t))t≥0 is C0 -semigroup be generated by A. We will give some sufficient conditions for uniformly stable and asymptotic equivalence of above equations.