To handle inequality state constraints in nonlinear optimal control problems, we propose a method of introducing an auxiliary state variable for each constraint. The derivatives of these state constraint variables are made positive if the constraint is violated, and zero if there is no constraint violation. By incorporating these state variables then as penalty functions in an augmented performance index, we can ensure that the inequality state constraints are satisfied everywhere inside the given time interval. The procedure, as illustrated and tested with three nonlinear optimal control problems, is found to work well even in the presence of many state constraints.