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We classify the pairs $(A,D)$ consisting of an$(\epsilon,\Gamma)$-olor-commutative associative algebra $A$ with an identityelement over an algebraically closed field $F$ of characteristic zero and afinite dimensional subspace $D$ of $(\epsilon,\Gamma)$-color-commutativelocally finite color-derivations of $A$ such that $A$ is $\Gamma$-graded$D$-simple and the eigenspaces for elements of $D$ are $\Gamma$-graded. Suchpairs are the important ingredients in constructing some simple Lie coloralgebras which are in general not finitely-graded. As some applications, usingsuch pairs, we construct new explicit simple Lie color algebras of generalizedWitt type, Weyl type.Comment: 15 page

Classification of derivation-simple color algebras related to locally finite derivations