  We describe a method which allows one to study hidden symmetries in a large
class of strongly coupled supersymmetric gauge theories in three dimensions. We
apply this method to the ABJM theory and to the infrared limit of N=4 SQCD with
adjoint and fundamental matter. We show that the U(N) ABJM model with
Chern-Simons level k=1 or k=2 has hidden N=8 supersymmetry. Hidden
supersymmetry is also shown to occur in N=4 d=3 SQCD with one fundamental and
one adjoint hypermultiplet. The latter theory, as well as the U(N) ABJM theory
at k=1, are shown to have a decoupled free sector. This provides evidence that
both models are dual to the infrared limit of N=8 U(N) super-Yang-Mills theory.
