  General asymptotic approach to the stability problem of multi-parameter
solitons in Hamiltonian systems $i\partial E_n/\partial z=\delta H/\delta
E_n^*$ has been developed. It has been shown that asymptotic study of the
soliton stability can be reduced to the calculation of a certain sequence of
the determinants, where the famous determinant of the matrix consisting from
the derivatives of the system invariants with respect to the soliton parameters
is just the first in the series. The presented approach gives first analytical
criterion for the oscillatory instability and also predicts novel stationary
instability. Higher order approximations allow to calculate corresponding
eigenvalues with arbitrary accuracy.
