[For part I see ibid. No. 3, 161-174 (1992; Zbl 0770.34042).] Properties of the sets \({\mathcal H} (x_ 0)\) of solutions of differential inclusions \(\dot x(t) \in Ax(t)+F(t,x(t))\), \(x(t_ 0)=x_ 0\) are investigated, where \(x\) belong to a Banach space. A few cases of operators \(A\) \((m\)-dissipative with compact semigroup, infinitesimal generator of a compact semigroup,...) are considered, \(F\) is upper semicontinuous in \(x\) (plus some additional conditions). The following types of results are given: existence of solutions, connectedness of \({\mathcal H} (x_ 0)\), \({\mathcal H} (x_ 0)\) are \(R_ \delta\) (intersections of compact, absolute retracts) and upper semicontinuity of \({\mathcal H} (x_ 0)\) with respect to \(x_ 0\).