  The purpose of this article is to study an $f$-cosymplectic manifold $M$
admitting Ricci solitons. Here we consider mainly two classes of Ricci solitons
on $f$-cosymplectic manifolds. One is the class of contact Ricci solitons. The
other is the class of gradient Ricci solitons, for which we give the local
classifications of $M$. Meanwhile, we also give some properties of
$f$-cosymplectic manifolds.
