Summary: We consider marginal deformations of the superconformal ABJM/ABJ models which preserve \( \mathcal{N} = 2 \) supersymmetry. We determine perturbatively the spectrum of fixed points and study their infrared stability. We find a closed line of fixed points which is IR stable. The fixed point corresponding to the ABJM/ABJ models is stable under marginal deformations which respect the original \(SU(2)_{A } \times SU(2)_{B }\) invariance, while deformations which break this group destabilize the theory which then flows to a less symmetric fixed point. We discuss the addition of flavor degrees of freedom. We prove that in general a flavor marginal superpotential does not destabilize the system in the IR. An exception is represented by a marginal coupling which mixes matter charged under different gauge sectors. Finally, we consider the case of relevant deformations which should drive the system to a strongly coupled IR fixed point recently investigated in [D. Martelli and J. Sparks, ibid. 2009, No.12, Article ID 017 (2009); http://arxiv.org/abs/0909.2036 [hep-th]].