  We construct the classical action of the Aharony-Bergman-Jafferis-Maldacena
(ABJM) model in the N=3, d=3 harmonic superspace. In such a formulation three
out of six supersymmetries are realized off shell while the other three mix the
superfields and close on shell. The superfield action involves two
hypermultiplet superfields in the bifundamental representation of the gauge
group and two Chern-Simons gauge superfields corresponding to the left and
right gauge groups. The N=3 superconformal invariance allows only for a minimal
gauge interaction of the hypermultiplets. Amazingly, the correct sextic scalar
potential of ABJM emerges after the elimination of auxiliary fields. Besides
the original U(N)xU(N) ABJM model, we also construct N=3 superfield
formulations of some generalizations. For the SU(2)xSU(2) case we give a simple
superfield proof of its enhanced N=8 supersymmetry and SO(8) R-symmetry.
