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We introduce the notion of a crystal base of a finite dimensional q-deformedKac module over the quantum superalgebra $U_q(\gl(m|n))$, and prove itsexistence and uniqueness. In particular, we obtain the crystal base of a finitedimensional irreducible $U_q(\gl(m|n))$-module with typical highest weight. Wealso show that the crystal base of a q-deformed Kac module is compatible withthat of its irreducible quotient $V(\lambda)$ given by Benkart, Kang andKashiwara when $V(\lambda)$ is an irreducible polynomial representation.

Crystal bases of q-deformed Kac modules over the quantum superalgebra $U_q(\gl(m|n))$