Analytic Approaches to the Evolution of Polarised Parton Distributions at Small $x$

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.