  Group Field Theories (GFT) are quantum field theories over group manifolds;
they can be seen as a generalization of matrix models. GFT Feynman graphs are
tensor graphs generalizing ribbon graphs (or combinatorial maps); these graphs
are dual not only to manifolds. In order to simplify the topological structure
of these various singularities, colored GFT was recently introduced and
intensively studied since. We propose here a different simplification of GFT,
which we call multi-orientable GFT.
  We study the relation between multi-orientable GFT Feynman graphs and
colorable graphs. We prove that tadfaces and some generalized tadpoles are
absent. Some Feynman amplitude computations are performed. A few remarks on the
renormalizability of both multi-orientable and colorable GFT are made. A
generalization from three-dimensional to four-dimensional theories is also
proposed.
