  We generalize a recently developed ADHMN-like construction of self-dual
string solitons using loop space. In particular, we present two extensions: The
first one starts from solutions to the Basu-Harvey equation for the ABJM model,
the second one starts from solutions to a corresponding BPS equation in an N=2
supersymmetric deformation of the BLG model. Both constructions yield solutions
to the abelian and the nonabelian self-dual string equation transgressed to
loop space. These equations might provide an effective description of M2-branes
suspended between M5-branes.
