The known Levitan’s Theorem states that the finite-dimensional linear differential equationwith Bohr almost periodic coefficients A(t) and f(t) admits at least one Levitan almost periodic solution if it has a bounded solution. The main assumption in this theorem is the separation among bounded solutions of homogeneous equationsIn this paper we prove that infinite-dimensional linear differential equation (1) with Levitan almost periodic coefficients has a Levitan almost periodic solution, if it has at least one relatively compact solution and the trivial solution of equation (2) is Lyapunov stable.