A semimodule T is named ss-supplemented if all subsemimodule N of T have supplement L in T such that N ∩ L is semisimple. T is named strongly local if Rad(T) is semisimple and T is local. It is shown that every strongly local semimodule is amply ss-supplemented. If T is an ss-supplemented p-projective subtractive semimodule, at that time T is amply ss-supplemented.