The pre-big-bang cosmology inspired by superstring theories has been s
uggested as an alternative to slow-roll inflation. We analyze, in both
the Jordan and Einstein frames, the effect of spatial curvature on th
is scenario and show that too much curvature - of either sign - reduce
s the duration of the inflationary era to such an extent that the flat
ness and horizon problems are not solved. Hence, a fine-tuning of init
ial conditions is required to obtain enough inflation to solve the cos
mological problems. [S0556-2821(97)01020-5].