  This paper introduces and studies a field theoretic analogue of the Clebsch
variational principle of classical mechanics. This principle yields an
alternative derivation of the covariant Euler-Poincar\'e equations that
naturally includes covariant Clebsch variables via multisymplectic momentum
maps. In the case of diffeomorphism groups, this approach gives a new
interpretation of recently derived singular peakon solutions of Diff(R)-strand
equations, and allows for the construction of singular solutions (such as
filaments or sheets) for a more general class of equations, called covariant
EPDiff equations. The relation between the covariant Clebsch principle and
other variational principles arising in mechanics and field theories, such as
Hamilton-Pontryagin principles, is explained through the introduction of a
class of covariant Pontryagin variational principles in field theories.
