  We infer the star formation history in different regions of the blue compact
dwarf NGC 1705 by comparing synthetic color-magnitude diagrams with HST optical
and near-infrared photometry. We find that NGC 1705 is not a young galaxy
because its star formation commenced at least 5 Gyr ago. On the other hand, we
confirm the existence of a recent burst of star formation between 15 and 10 Myr
ago. We also find evidence for new strong activity, which started 3 Myr ago and
is still continuing. The old population is spread across the entire galaxy,
while the young and intermediate stars are more concentrated in the central
regions. We derive an almost continuous star formation with variable rate, and
exclude the presence of long quiescent phases between the episodes during the
last ~1 Gyr. The central regions experienced an episode of star formation of
\~0.07 Msun/yr (for a Salpeter initial mass function [IMF]) 15 to 10 Myr ago.
This coincides with the strong activity in the central super star cluster. We
find a rate of ~0.3 Msun/yr for the youngest ongoing burst which started ~3 Myr
ago. This is higher than in other dwarfs and comparable to the rate of NGC
1569. The star formation rate of earlier episodes is not especially high and
falls in the range 10^{-3}-10^{-1} Msun/yr. The IMF is close to the Salpeter
value or slightly steeper.
