Let K be a closed convex cone with the nonempty interior in a real Banach space and let cc(K) denote the family of all nonempty convex compact subsets of K. Assume that continuous linear multifunctions H, ψ : K -> cc(K) are given. We consider the following problem D2 φ (t, x) = φ (t, H(x)), D φ (t,x) / (t=0) = {0}, φ (0, x) = ψ (x) for t ≥ 0 and [formula], where D φ (t, x) denotes the Hukuhara derivative of φ (t, x) with respect to t.