SU(n)_cotimes SU(m)_Lotimes U(1)_N generalizations of the Standard Model

We consider generalizations of the standard model (SM) which are based on the gauge symmetry $SU(n)_c\otimes SU(m)_L\otimes U(1)_N$. Although the most interesting possibilities occur when $n=3$, we will consider also the cases $n=4,5$ both with $m=3,4$. Models with left-right symmetry, horizontal symmetries and the possible embedding in a larger group (grand unification scenarios) are briefly discussed.