We consider a new large-N limit, in which the 't Hooft coupling grows with N. We argue that a class of large-N equivalences, which is known to hold in the 't Hooft limit, can be extended to this very strongly coupled limit. Hence this limit may lead to a new way of studying corrections to the 't Hooft limit, while keeping nice properties of the latter. As a concrete example, we describe large-N equivalences between the ABJM theory and its orientifold projection. The quivalence implies that operators neutral under the projection symmetry have the same correlation functions in two theories at large-N. Usual field theory arguments are valid when 't Hooft coupling \lambda\sim N/k is fixed and observables can be computed by using a planar diagrammatic expansion. With the help of the AdS/CFT correspondence, we argue that the equivalence extends to stronger coupling regions, N >> k, including the M-theory region N >> k^5. In the second part of the talk, we pursue the equivalence between supersymmetric Chern-Simons-matter theories and consider the other orbifold equivalence between quiver Chern-Simons- matter theories including flavors which have gravity duals.