  We investigate particular models which can be N-fold supersymmetric at
specific values of a parameter in the Hamiltonians. The models to be
investigated are a periodic potential and a parity-symmetric sextic triple-well
potential. Through the quantitative analyses on the non-perturbative
contributions to the spectra by the use of the valley method, we show how the
characteristic features of N-fold supersymmetry which have been previously
reported by the authors can be observed. We also clarify the difference between
quasi-exactly solvable and quasi-perturbatively solvable case in view of the
dynamical property, that is, dynamical N-fold supersymmetry breaking.
