The Brundsen-Holmes method of power spectrum estimation for the Duffin
g-Holmes oscillator is applied to the case of weak quasiperiodic excit
ation and then extended to weak colored noise excitation with any spec
ified spectral density. A novel model of near-Gaussian noise is introd
uced to achieve this extension. The results obtained by this approach
coincide with and extend those obtained by Stone and Holmes' applicati
on of the Fokker-Planck equation. In particular, our results confirm S
tone's conjecture that the expression for the mean time between succes
sive maxima in the case of colored noise is similar to that for white
noise.