  The aim of this paper is to develop a constraint algorithm for singular
classical field theories in the framework of $k$-cosymplectic geometry. Since
these field theories are singular, we need to introduce the notion of
$k$-precosymplectic structure, which is a generalization of the
$k$-cosymplectic structure. Next $k$-precosymplectic Hamiltonian systems are
introduced in order to describe singular field theories, both in Lagrangian and
Hamiltonian formalisms. Finally, we develop a constraint algorithm in order to
find a submanifold where the existence of solutions of the field equations is
ensured. The case of affine Lagrangians is studied as a relevant example.
