Within the scope of Gaussian equivalent linearization, a new probabili
stic criterion for determining the coefficients of the linearized equi
valent equation is proposed to treat stationary responses of dan-linea
r systems under zero mean Gaussian random excitation. Applications to
the Duffing and Van der Pol oscillators subjected to white noise are p
resented that show significant improvement over corresponding accuracy
of the classical Gaussian equivalent linearization for hath weak and
strong non-linearity.