Backward stimulated Raman and Brillouin scattering (SRS and SBS) are experimentally investigated by using two successive 1-μm, 1.5-ps FWHM laser pulses. The collinear pulses, separated by 3 or 6 ps and of moderate laser intensities (∼2×10^{16}Wcm^{-2}), are fired into a preionized He plasma of density ∼2.5-6×10^{19}cm^{-3}. The electron plasma waves and ion acoustic waves, respectively driven by SRS and SBS, are analyzed through space- and time-resolved Thomson scattering. Depending on the laser and plasma parameters, we observe the effect of the first pulse on the time-resolved SRS and SBS signals of the second pulse. The measurements are found to qualitatively agree with the results of a large-scale particle-in-cell simulation.