The accurate transient probability density functions (PDFs) of the non-smoothly dynamical systems driven by both multiplicative and additive modulated stochastic excitations are obtained and investigated for the first time. The exponential-polynomial-closure method is adopted to solve the Fokker–Planck–Kolmogorov (FPK) equations formulated for the considered systems. The time-variant residual error is made zero with a group of weighting functions. The solution accuracy and running efficiency of the presented procedure are verified with reference to Monte Carlo simulation (MCS). By comparing those PDFs of responses achieved by different techniques, some interesting phenomena are observed. The first is that the nonlinear behaviors of the oscillators can become stronger and stronger over time as the response variances approach their maximum values during the evolutionary process because of the presence of modulated stochastic excitations. The second is that the non-Gaussian behaviors of the responses can be influenced by the Gaussian-distributed initial responses, which is one of the features in the transient stochastic evolutionary analysis. Moreover, the achieved transient PDFs can be asymmetrical when the modulated stochastic excitations are correlated.