  Within the framework of the hypothesis offered by authors about a
complex-valued nature of physical quantities the stability of basic equations
of the classical physics concerning complex-valued perturbations of parameters
and boundary conditions is explored. The conducted examination of nonlinear
equations and, what is more important, of linear differential equations shows
violation in some cases of the continuous dependence of the solution on the
change of imaginary parts of parameters and boundary conditions in the
neighborhood of zero. In other words, it was revealed that a small imaginary
part may drive the real solution. It may be concluded that a small imaginary
part, even if unobservable, is still an inherent characteristic of a physical
quantity, being yet something like a hidden parameter, and manifests itself
only indirectly forcing the system to move in this or that direction, which may
be taken as a basis for experimental testing of the put forward hypothesis
about a complex-valued nature of physical quantities.
