  A remarkable feature of the models with interactions exhibiting higher-spin
(HS) gauge symmetries in $d>2$ is that their most symmetric vacua require
(anti)-de Sitter (AdS) geometry rather than the flat one. In striking
parallelism to what might be expected of M theory HS gauge theories describe
infinite towers of fields of all spins and possess naturally space-time SUSY
and Chan-Paton type inner symmetries. In this paper, we analyze at the level of
the equations of motion the simplest non-trivial HS model which describes HS
gauge interactions (on the top of the usual supergravitational and
(Chern-Simons) Yang-Mills interactions) of massive spin-0 and spin-1/2 matter
fields in d=2+1 AdS space-time. The parameter of mass of the matter fields is
identified with the vev of a certain auxiliary field in the model. The matter
fields are shown to be arranged into d3 N=2 massive hypermultiplets in certain
representations of $U(n)\times U(m)$ Yang-Mills gauge groups. Discrete
symmetries of the full system are studied, and the related N=1 supersymmetric
truncations with O(n) and Sp(n) Yang-Mills symmetries are constructed. The
simplicity of the model allows us to elucidate some general properties of the
HS models. In particular, a new result, which can have interesting implications
to the higher-dimensional models, is that our model is shown to admit an
"integrating" flow that proves existence of a non-local B\"acklund-Nicolai-type
mapping to the free system.
