In this paper we show that, for optimal control problems involving equality and inequality constraints on the control function, the notions of normality and properness (or the Mangasarian-Fromovitz constraint qualification) of a trajectory relative to the set of constraints are equivalent. This is in contrast with some differences recently obtained between the theories of mathematical programming and optimal control, and it provides an important insight in the derivation of first and second order necessary optimality conditions for infinite dimensional problems.