The authors give the manifestly off-shell supersymmetric gauge-fixed actions for (1, 0) and (1, 1) supergravity theories in terms of unconstrained superfields. This is carried out for gauges which include the harmonic as well as the superconformal gauges. It is shown that there is a non-trivial interplay between the WZ gauge on the world sheet, the BRST operator and the superconformal gauge-fixing condition.