Given a unitary character \(\mu: G \rightarrow \mathbf{C}\) and an involution \(\sigma\) of a group G, we study the Hyers–Ulam–Rassias stability of Wilson’s functional equations: $$\displaystyle\begin{array}{rcl} & f(xy) +\mu (y)f(x\sigma (y)) = 2f(x)g(y),\;x,y \in G,& {}\\ & f(xy) +\mu (y)f(x\sigma (y)) = 2g(x)f(y),\;x,y \in G.& {}\\ \end{array}$$ As a consequence, we find the superstability of d’Alembert’s functional equation: $$\displaystyle{g(xy) +\mu (y)g(x\sigma (y)) = 2g(x)g(y),\;x,y \in G.}$$