This paper deals with initial-regular oblique derivative boundary value problems for nonlinear parabolic complex equations of second order in a multiply connected domain, where coefficients of equations are measurable. We first verify the uniqueness of solution for above problems, and then give a priori estimates of solutions for the problems. Finally, by using the above estimates and the method of parameter extension, the existence of solutions of initial-boundary value problems is proved. The results in this paper are the development of corresponding theorems in [1, 4, 5], here the condition (1.4) is weaker than the corresponding condition in [1, 5], i.e. the constant 4/3 in [1, 5] is replaced by 3/2 in (1.4).