The photoluminescence (PL) spectra of CdTe/ZnTe double quantum wells (QWs) are studied on a series of samples containing two CdTe layers with nominal thicknesses of 2 and 4 monolayers (ML) in the ZnTe matrix. The QWs were grown in atomic-layer epitaxy and separated by ZnTe spacers with the thicknesses dsp=40−160 ML. The dependences of the relative intensity of shallow QW1 and deep QW2 PL bands (I1 and I2, respectively) on the pump intensity (J) when excited by the lasers with different radiation wavelengths are investigated. It is found that in the sample with dsp=40 ML, the ratio Y(J)=I1/I2 depends on J and the shape of the Y(J) dependency changes with the excitation wavelength. In the samples with dsp > 70 ML Y(J) also changes with the excitation intensity J, but the shape of this dependence is the same for various excitation wavelengths. It is concluded that the energy relaxation in these samples is influenced not only by the tunneling of charge carriers from QW1 to QW2, but also by carrier relaxation at the nonradiative centers, for which the recombination rate is different for shallow and deep QWs.