A two-country model of growth is developed with exogenous fluctuations in the rate of technological progress. Technological growth in the leading country follows a random walk, while in the lagging country the rate of advance depends on the technological distance between the two countries and the efficiency of limitation. In the absence of cyclical technological change or lags in technology transfer, there is monotonic convergence in income levels. If the two countries share initially identical technologies, their standards of living never diverge. In the presence of cyclical technological change and lags of limitation, a rich pattern of relative growth emerges: the model generates convergence, divergence and leapfrogging along balanced growth equilibria, and also demonstrates why observed convergence rates may be substantially slower than those predicted by the standard neoclassical model.