A generalization of the SU(2) spin systems on a lattice and their cont
inuum limit to an arbitrary compact group G is discussed. The continuu
m limits are, in general, nonrelativistic sigma-model-type field theor
ies targeted on a homogeneous space G/H, where H contains the maximal
torus of G. In the ferromagnetic case the equations of motion derived
from our continuum Lagrangian generalize the Landau-Lifshitz equations
with quadratic dispersion relation for small wave vectors. In the ant
iferromagnetic case the dispersion law is always linear in the long-wa
velength limit. The models become relativistic only when G/H is a symm
etric space. Also discussed are a generalization of the Holstein-Prima
koff representation of the SU(N) algebra, the topological term, and th
e existence of the instanton-type solutions in the continuum limit of
the antiferromagnetic systems.