Suppose B is a bounded linear operator in a Banach space. If the differential operator d n d t n − B has a Bohr-Neugebauer type property for Bochner almost periodic functions, then, for any Stepanov almost periodic continuous function g ( t ) and any Stepanov-bounded solution of the differential equation d n d t n u ( t ) − B u ( t ) = g ( t ) , u ( n − 1 ) , … , u ′ , u are all almost periodic.