  We present exact ground states in spin models with orbital generacy in one
and higher dimensions. A method to obtain the exact ground states of the models
when the Hamiltonians are composed of the products of two commutable operators
is proposed. For the case of the spin-1/2 model with two-fold degeneracy some
exact ground states are given, such as the Valence-Bond (VB), the magnetically
ordered, and the orbitally ordered states under particular parameter regimes.
We also find the models with the higher spin and degeneracy which have the new
types of VB ground states in the spin and the orbital sectors.
