This paper considers three types of redundant constraints in systems of an arbitrary number of inequalities posed on real locally convex spaces. The properties of each class of redundant constraints are analized and different classification criteria are given, some of them extending well-known redundancy tests for ordinary linear systems. The paper also provides results for more paticular families of linear systems, for instance, systems with either finitely many unknowns (constraints systems in semi-infinite optimization) or finitely many inequalities (constraints systems in certain moment problems)