  Homogenization of integral functionals is studied under the constraint that
admissible maps have to take their values into a given smooth manifold. The
notion of tangential homogenization is defined by analogy with the tangential
quasiconvexity introduced by Dacorogna, Fonseca, Maly and Trivisa \cite{DFMT}.
For energies with superlinear or linear growth, a $\Gamma$-convergence result
is established in Sobolev spaces, the homogenization problem in the space of
functions of bounded variation being the object of \cite{BM}.
