  We focus on the presence of almost automorphy in strongly monotone
skew-product semiflows on Banach spaces. Under the $C^1$-smoothness assumption,
it is shown that any linearly stable minimal set must be almost automorphic.
This extends the celebrated result of Shen and Yi [Mem. Amer. Math. Soc.
136(1998), No. 647] for the classical $C^{1,\alpha}$-smooth systems. Based on
this, one can reduce the regularity of the almost periodically forced
differential equations and obtain the almost automorphic phenomena in a wider
range.
