  We study marginal deformations of superconformal Chern-Simons matter theories
that are based on 3-algebras. For this, we introduce the notion of an
associated 3-product, which captures very general gauge invariant deformations
of the superpotentials of the BLG and ABJM models. We also consider conformal
multi-trace deformations preserving N=2 supersymmetry. We then use N=2
supergraph techniques to compute the two-loop beta functions of these
deformations. Besides confirming conformal invariance of both the BLG and ABJM
models, we also verify that the recently proposed beta-deformations of the ABJM
model are indeed marginal to the order we are considering.
