  The notions of Lie color 2-algebras and 2-term color L-infty-algebras over a
group-graded vector space are introduced and studied. It is proved that the
category of Lie color 2-algebras and the category of 2-term color L1-algebras
are equivalent. We construct Lie color 2-algebras from omni-Lie color algebras
and Leibniz color algebras. Some example of $Z^2_2$ -graded Lie color
2-algebras are given.
