  Using general construction of star-product the q-deformed Wigner-Weyl-Moyal
quantization procedure is elaborated. The q-deformed Groenewold kernel
determining the product of quantum observables is given in explicit form for
small nonlinearities corresponding to nonlinear vibrations of classical and
quantum q-oscillators. The deformations of Groenewold kernel related to general
kinds of nonlinear vibrations described by f-oscillators are considered.

Quantum Physics