Conditions are given for the stability of multistep methods that vary the stepsize using the interpolation technique of Nordsieck. If the stepsize selection function is variation-bounded, then these methods are stable. Alternatively there exist constants a, b, c depending on the method and satisfying $a \leqq b < 1 < c$ such that if the stepsize ratio ${{h_{n + 1} } / {h_n }}$ satisfies either ${{0 < h_{n + 1} } / {h_n \leqq a}}$ or ${{b < h_{n + 1} } / {h_n \leqq c}}$ then the method is stable.As the frequency of stepsize changing decreases, the methods become more stable in the sense that the intervals defined by a, b, and c are larger. Tables and graphs are given for the Adams and backward differentiation methods indicating how stability changes with frequency of changing stepsize. In particular, it is shown that $(k + 1)$-value Adams formulas $(k \leqq 6)$ are stable for ${{0 < h_{n + 1} } / {h_n \leqq c}}$; that is, it is shown that stability is maintained whenever the stepsize is decreased by an arb...