For forensic investigation of dyes used in the textile dying industry by Raman spectroscopy, the capability to discriminate several dyes is significant. When trace samples of fibres tainted with unknown dyes have to be confronted to a reference material, the minor dye is typically present in less than 10 wt% in the dyeing preparations. In the present study, we investigate the ability of Raman spectroscopy to discriminate two dyes in binary mixtures. 50 mixtures were prepared from a selection of five textile dyes in various molar proportion. They were systematically studied with two excitation laser sources at 514 nm and at 785 nm, both referenced in the forensic fibre literature. Representative data were obtained for different scenario's considering the relative capability of each dye to lead to high or weak Raman signal as well as possible fluorescence emission. In particular, we discuss the complementarity of the data obtained with both lasers and the supervised data exploratory treatments leading to the detection of the dye signal: from the simple observation by the operator, the search in spectral databases to the quantitative spectral subtraction of the dominant dye contribution.