  We study the structure of profinite polyadic groups and we prove that a
polyadic topological group $(G, f)$ is profinite, if and only if, it is
compact, Hausdorff, totally disconnected. More generally, for a pseudo-variety
(or a formation) of finite groups $\mathfrak{X}$, we define the class of
$\mathfrak{X}$-polyadic groups, and we show that a polyadic group $(G, f)$ is
pro-$\mathfrak{X}$, if and only if, it is compact, Hausdorff, totally
disconnected and for every open congruence $R$, the quotient $(G/R, f_R)$ is
$\mathfrak{X}$-polyadic.
