  Though the irreducible representations of the Poincare' group form the
groundwork for the formulation of relativistic quantum theories of a particle,
robust classes of such representations are missed in current formulations of
these theories. In this work the extended class of irreducible representations
with positive `mass' parameter is explicitly determined. Several new
representations in such extension, so far excluded, give rise to consistent
theories for Klein-Gordon particles and also to new species of particle
theories.
