  The instability in the cosmic-ray precursor of a supernova shock moving in
interstellar medium is studied. The level of magnetohydrodynamic turbulence in
this region determines the maximum energy of particles accelerated by the
diffusive shock acceleration mechanism. The high efficiency of cosmic ray
acceleration is accepted, and the consideration is not limited by the case of
weak turbulence. It is assumed that Kolmogorov type nonlinear wave interactions
together with the ion-neutral collisions restrict the amplitude of random
magnetic field. As a result, the maximum energy of accelerated particles
strongly depends on the age of supernova remnant. The maximum energy can be as
high as $\sim10^{17}Z$ eV in young supernova remnants and falls down to about
$\sim10^{10}Z$ eV at the end of Sedov stage. Thus the standard estimate of
maximum particle energy based on the Bohm limit calculated for the interstellar
magnetic field strength is not justified in this case. This finding may explain
why the supernova remnants with the age more than a few thousand years are not
prominent sources of very high energy gamma-rays.
