  The k-symplectic formulation of field theories is especially simple, since
only tangent and cotangent bundles are needed in its description. Its defining
elements show a close relationship with those in the symplectic formulation of
mechanics. It will be shown that this relationship also stands in the
presymplectic case. In a natural way, one can mimick the presymplectic
constraint algorithm to obtain a constraint algorithm that can be applied to
$k$-presymplectic field theory, and more particularly to the Lagrangian and
Hamiltonian formulations of field theories defined by a singular Lagrangian, as
well as to the unified Lagrangian-Hamiltonian formalism (Skinner--Rusk
formalism) for k-presymplectic field theory. Two examples of application of the
algorithm are also analyzed.
