Abstract
We construct a new off-shell N=4, d=3 nonlinear vector supermultiplet. The irreducibility constraints for the superfields leave in this supermultiplet the same component content as in the ordinary linear vector supermultiplet. We present the most general sigma-model type action for the N=4, d=3 electrodynamics with the nonlinear vector supermultiplet, which despite the nonlinearity of the supermultiplet may be written as an integral over a chiral superspace. This action shares the most important properties with its linear counterpart. We also perform the dualization of the vector component into a scalar one and find the corresponding N=4, d=3 supersymmetric action which describes new hyper-Kaehler sigma-model in the bosonic sector.
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