The Lau effect refers to interference phenomenon involving double-grating system illuminated by an extended white light source and it has received wide attention. Until now, the Lau effect has been studied regarding double-grating system immersed in homogenous media. A generalization of Lau effect to the case of a GRIN medium is considered. We present an explanation based on the coherence theory. We begin the analysis by describing, in general terms, the propagation of the second-order field correlations in GRIN media, via the cross-spectral density function. This provides the basics for discussing the evolution of the intensity distribution and the cross-spectral density function of the field incident on the second grating. The particular case of a selfoc GRIN medium and two sinusoidal gratings is analyzed.