Summary: Let \(F\) and \(G\) be finitely generated groups of polynomial growth with the degrees of polynomial growth \(d(F)\) and \(d(G)\) respectively. Let \(S = \{S^f\}_{f\in F}\) be a continuous action of \(F\) on a compact metric space \(X\) with a positive topological entropy \(h(S)\). Then (i) there are no expansive continuous actions of \(G\) on \(X\) commuting with \(S\) if \(d(G)<d(F)\); (ii) every expansive continuous action of \(G\) on \(X\) commuting with \(S\) has positive topological entropy if \(d(G)=d(F)\).