We report results of a detailed study of the nearby blue compact dwarf galaxy NGC 1705. There are two stellar populations in NGC 1705: an underlying population around a Gyr old or older, and a young population of fairly continuous star formation for the last 250 Myr. An off-centre nucleus, which is probably a young (10 Myr old), massive (106M⊙) globular cluster, is part of this young population. The Hα morphology and emission line kinematics are consistent with an expulsive flow triggered by the formation of the nucleus. We show that NGC 1705 is losing ionized material in this galactic wind with neutral material probably entrained in the flow. This flow may lead to total removal of the ISM. The evolutionary fate of NGC 1705 is uncertain but the most likely outcome is rapid evolution into a nucleated dwarf elliptical galaxy.