We construct a scalar, first order, almost periodic
ODE
(
∗
)
x
+
A
(
t
)
x
=
B
(
t
)
{\text {ODE}}( * )x + A(t)x = B(t)
which admits bounded solutions, but no almost periodic solutions. Using this equation, we give an example of a two-dimensional, almost periodic system whose projective flow admits two minimal subsets, one of which is almost automorphic but not almost periodic. Finally, we show that some equation in the hull of
(
∗
)
( * )
admits an almost automorphic, nonalmost periodic solution.