  When a droplet spreads on a solid substrate, it is unclear what are the
correct boundary conditions to impose at the moving contact line. The classical
no-slip condition is generally acknowledged to lead to a non-integrable
singularity at the moving contact line, for which a slip condition, associated
with a small slip parameter, $\lambda$, serves to alleviate. In this paper, we
discuss what occurs as the slip parameter, $\lambda$, tends to zero. In
particular, we explain how the zero-slip limit should be discussed in
consideration of two distinguished:: one where time is held constant $t =
O(1)$, and one where time tends to infinity at the rate $t = O(|\log
\lambda|)$. The crucial result is that in the case where time is held constant,
the $\lambda \to 0$ limit converges to the slip-free equation, and contact line
slippage occurs as a regular perturbative effect. However, if $\lambda \to 0$
and $t \to \infty$, then contact line slippage is a leading-order singular
effect.
