  Let $p \geqslant 3$ be a prime number and let $n \geqslant 0$ be an integer
such that $p-1$ divides $n.$ In this short note we construct a family of
$(p,n)$-gonal Riemann surfaces of maximal genus $2np+(p-1)^2$ with more than
one $(p,n)$-gonal group.
