We present results of a detailed study aiming at understanding to what precision star formation histories (SFHs) can be determined for distant galaxies observable in integrated light only. Using our evolutionary synthesis code, we have performed a set of simulations of galaxies with a wide range of different SFHs. By analysing the resulting colors, spectra and Lick indices, we investigate to which extent different SF scenarios can be discriminated on the basis of their photometric and spectral properties, respectively. We find the robust result that no later than 4 Gyrs after the latest episode of enhanced star formation all scenarios exhibit very similar colors and indices; in practice, it is not possible to distinguish different scenarios of star formation which have evolved for more than 1, at the utmost 3-4 Gyrs since the last star forming event, even when using spectral indices. For how long different SF scenarios can be disentangled highly depends on the range of colors available and absorption lines considered, as well as on the details of the SFHs to be compared.
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