  In this paper we consider the frame-like formulation for the so called
infinite (continuous) spin representations of the Poincare algebra. In the
three dimensional case we give explicit Lagrangian formulation for bosonic and
fermionic infinite spin fields (including the complete sets of the gauge
invariant objects and all the necessary extra fields). Moreover we find the
supertransformations for the supermultiplet containing one bosonic and one
fermionic fields leaving the sum of their Lagrangians invariant. Properties of
such fields and supermultiplets in four and higher dimensions are also briefly
discussed.
