We compute the spectrum of relic gravitons in a model of string cosmol
ogy. In the low- and high-frequency limits we reproduce known results.
The full spectrum, however, also displays a series of oscillations wh
ich could give a characteristic signature at the planned LIGO-VIRGO de
tectors. For special values of the parameters of the model the signal
reaches its maximum already at frequencies accessible to LIGO and VIRG
O and it is close to the sensitivity of first generation experiments.