The general convergence theory of [1] and a stability functional introduced in [2] are used to analyze the stability and order of consistency of linear multistep methods for Volterra functional differential equations. The techniques used require weaker continuity conditions than have been used before. For example, considering the equation \[ y'(t) = f(t,y(t),y(\alpha (t)),\int_0^t {w(t,s,y(s))ds} ), \]$0 \leqq \alpha (t) \leqq t \leqq 1$, where f is Lipschitz continuous in its second, third and fourth arguments; and using a linear pth order multistep method that satisfies the weak stability root condition, it is proved that the method converges if $y'(t)$ and $w(t,s,y(s))$ are Riemann integrable, and has order $O(h^p )$ convergence if $y^{(p - 1)} (t)$ and $({\partial / {\partial s}})^{p - 2} w(t,s,y(s))$ are the integrals of functions of bounded variation. There is no requirement that either f, $\alpha $ or w be continuous functions of t. The results apply for a function y taking on values in any real vector space, finite- or infinite-dimensional.