We infer the star formation history in different regions of the blue compact dwarf NGCÂ 1705 by comparing synthetic color-magnitude diagrams with HST optical and near-infrared photometry . We find that NGCÂ 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 \approx 1 Gyr . The central regions experienced an episode of star formation of \sim 0.07 M _ { \odot } yr ^ { -1 } ( 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 \sim 0.3 M _ { \odot } yr ^ { -1 } for the youngest ongoing burst which started \sim 3 Myr ago . This is higher than in other dwarfs and comparable to the rate of NGCÂ 1569 . The star formation rate of earlier episodes is not especially high and falls in the range 10 ^ { -3 } -10 ^ { -1 } M _ { \odot } yr ^ { -1 } . The IMF is close to the Salpeter value or slightly steeper .