  The $Q^2$ evolution of polarised parton distributions at small $x$ is
studied. Various analytic approximations are critically discussed. We compare
the full evolution with that obtained from the leading-pole approximation to
the splitting functions, and show that the validity of this approximation
depends critically on the $x \to 0$ behaviour of the starting distributions. A
new analytic solution which is valid at small $x$ is obtained, and its domain
of applicability is discussed.
