Аннотация:Bounded quasirepresentations always admit small (innorm) perturbations that define irreducible bounded quasirepresentations. Thepseudorepresentations corresponding to these quasirepresentations (if they exist) aredefined more rigidly, and therefore it is reasonable to seek for irreduciblepseudorepresentations. In this note, we describe the irreducible locally boundedfinite-dimensional pseudorepresentations of connected locally compact groups.