We establish an averaging principle on the real axis for semi-linear equation \(x'=\mu (\mathcal {A}x+F(t,x))\) with unbounded closed linear operator \(\mathcal {A}\) and Poisson stable (in particular, stationary, periodic, quasi-periodic, almost periodic, almost automorphic, and recurrent) coefficients. Under certain conditions, we prove that there is a unique solution that has the same character of recurrence as the coefficients in a small neighborhood of the stationary solution of the averaged equation. We prove that this solution converges to a stationary solution of the averaged equation uniformly on the real axis when the small parameter tends to zero.