This paper explores the use of a non-parametric frontier approach to analyse multi-factor productivity across time and countries. We argue that conventional measures of total factor productivity involve some restrictive assumptions that might bias the results. A non-parametric approach avoids these assumptions. The model uses linear programming techniques to examine the productivity catching-up in 14 OECD countries over the 1970-1990 period, under the assumption of variable returns to scale. We find evidence of convergence, even if at quite different speeds, for total industry, for manufacturing and for services.