  We investigate the radiation processes inside supernova remnants which are
powered by young pulsars. Using recent model for particle acceleration by the
pulsar wind nebulae, we obtain the equilibrium spectra of leptons and nuclei
inside the nebula as a function of time. We calculate the multiwavelength
photon spectra produced by leptons and nuclei and compare them with the
observations of the PWNe, i.e. the Crab Nebula, the Vela Supernova Remnant, and
the nebula around PSR 1706-44. It is found that the emission from the Crab
Nebula can be well fitted by the composition of the gamma-ray emission produced
by leptons and nuclei. The model is further tested by successful fitting of the
high energy spectrum from the Vela SNR. However, considered model does not give
good fitting to the emission from PSR1706-44, for the likely parameters of this
source, unless additional target for relativistic leptons is present inside the
nebula, e.g. the thermal infrared emission. Based on the knowledge obtained
from these fittings, we predict the gamma-ray fluxes in the TeV energy range
from other PWNe, i.e. MSH15-52 (PSR 1509-58), 3C58 (PSR J0205+6449), and CTB80
(PSR 1951+32).
