  The known Levitan's Theorem states that the linear differential equation $$
x'=A(t)x+f(t) \ \ \ (*) $$ with 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 equations $$ x'=A(t)x\ .\ \ \ (**) $$ In this paper we
prove that linear differential equation (*) with Levitan almost periodic
coefficients has a Levitan almost periodic solution, if it has at least one
bounded solution. In this case, the separation from zero of bounded solutions
of equation (**) is not assumed. The analogue of this result for difference
equations also is given.
  We study the problem of existence of Bohr/Levitan almost periodic solutions
for equation (*) in the framework of general nonautonomous dynamical systems
(cocycles).
