In single-molecule applications, the photostability of fluorescent molecules is a key parameter. We apply fluorescence correlation spectroscopy to compare the photostability of four fluorescein and four borondipyrromethene (BODIPY) dyes of similar structure but different triplet yields. The latter class of dyes are more stable. In the kinetic analysis the, diffusion and photobleaching are treated as competitive processes. Corrections, which account for saturation and for experimental artefacts, are achieved solely by using experimental data. Photobleaching is found to occur mainly through the first excited singlet state S(1), in contrast to previous findings.