We examine big bang nucleosynthesis (BBN) in models with a time-varying gravitational constant G, when this time variation is rapid on the scale of the expansion rate H, i.e, G˙/G≫H. Such models can arise naturally in the context of scalar-tensor theories of gravity and result in additional terms in the Friedman equation. We examine two representative models: a step-function evolution for G and a rapidly oscillating G.