  In this work it is studied the spontaneous breaking of superconformal and
gauge invariances in the Abelian N=1,2 three-dimensional supersymmetric
Chern-Simons-matter theories in a large N limit. It is computed the K\"ahlerian
effective superpotential at subleading order and shown that the
Coleman-Weinberg mechanism is the responsible for the dynamical generation of a
mass scale in the N=1 model. This effect appears due to two-loop diagrams that
are logarithmic divergent. In particular, the Coleman-Weinberg mechanism fails
when we lift the N=1 to N=2 Supersymmetric Chern-Simons-Matter model, like what
happens in a perturbative expansion in the coupling constants.
