The representations of an algebra of q-deformed paracommutation relations are discussed. The Bose quantization is shown to be exceptional among all possible para-Bose quantizations. Also it is demonstrated that the Ignatiev and Kuzmin oscillator (1987) is a particular case of the q-deformed paraoscillator.
Certain non-linear relations between the generators of the (q-deformed) Heisenberg algebra are found. Some of these relations are invariant under quantization and q-deformation.