We consider the dynamics of a protostellar disc in a binary system where th
e disc is misaligned with the orbital plane of the binary, with the aim of
determining the observational consequences for such systems. The disc wobbl
es with a period approximately equal to half the orbital period of the bina
ry and precesses on a longer time-scale. We determine the characteristic ti
me-scale for realignment of the disc with the orbital plane as a result of
dissipation. If the dissipation is determined by a simple isotropic viscosi
ty then we find, in line with previous studies, that the alignment time-sca
le is of the order of the viscous evolution time-scale. However, for typica
l protostellar disc parameters, if the disc tilt exceeds the opening angle
of the disc, then tidally induced shearing within the disc is transonic. In
general, hydrodynamic instabilities associated with the internally driven
shear result in extra dissipation that is expected to drastically reduce th
e alignment time-scale. For large disc tilts the alignment time-scale is th
en comparable with the precession time-scale, while for smaller tilt angles
delta, the alignment time-scale varies as (sin delta)(-1). We discuss the
consequences of the wobbling, precession and rapid realignment for observat
ions of protostellar jets and the implications for binary star formation me
chanisms.