Summary: We consider the Nemytskij operator, defined by \((N\phi)(x) := G(x, \phi(x))\), where \(G\) is a given set-valued function. It is shown that if \(N\) maps \(AC(I, C)\), the space of all absolutely continuous functions on the interval \(I := [0, 1]\) with values in a cone \(C\) in a reflexive Banach space, into \(AC(I, \mathcal K)\), the space of all absolutely continuous set-valued functions on \(I\) with values in the set \(\mathcal K\), consisting of all compact intervals (including degenerate ones) on the real line \(\mathbb R\), and \(N\) is uniformly continuous, then the generator \(G\) is of the form \[ G(x, y) = A(x)(y) + B(x) \] , where the function \(A(x)\) is additive and uniformly continuous for every \(x \in I\) and, moreover, the functions \(x \rightarrowtail A(x)(y)\) and \(B\) are absolutely continuous. Moreover, a condition, under which the Nemytskij operator maps the space \(AC(I, C)\) into \(AC(I, \mathcal K)\) and is Lipschitzian, is given.