In this sequence of work we investigate polynomial equations of additive functions. This is the continuation of the paper [5] entitled Polynomial equations for additive functions I. We consider here the solutions of the equation \(\begin{aligned} \sum _{i=1}^{n}f_{i}(x^{p_{i}})g_{i}(x)^{q_{i}}= 0 \qquad \left( x\in \mathbb {F}\right) , \end{aligned}\) where n is a positive integer, \(\mathbb {F}\subset \mathbb {C}\) is a field, \(f_{i}, g_{i}:\mathbb {F}\rightarrow \mathbb {C}\) are additive functions and \(p_i, q_i\) are positive integers for all \(i=1, \ldots , n\) . Using the theory of decomposable functions we describe the solutions as compositions of higher-order derivations and field homomorphisms. In many cases, we also give a tight upper bound for the order of the involved derivations. Moreover, we present the full description of the solutions in some important special cases, too.
