We give a version of the abstract Cauchy-Kovalevskaya Theorem for the Cauchy problem u'= A(t, u), u(O)=u0 when A is not necessarily a Lipschitz continuous operator. The operator A(t,u)= F(t,u,u) verifies 1) F:1 I x Br1,R x Br,R- X3 for s < r < ro (r1 < ro is fixed), F(t, u, .) is Lipschitz continuous, and F(t, ., ,) is alpha-Lipshitz continuous or 2 ) F : I x Br1 , R x X r - X 9 for s< r < ro (r1 < ro is fixed), and F(t, ., .) is alpha-Lipschitz continuous , where Br,R denotes the ball of radius R in Xr. We prove the result by using Tonelli approximations and fixed point theorems.