This is a paper on the Regional Convergence Hypothesis, applied to the Peruvian case during the 1978 – 1992 period. The research considers an important element, generally neglected by studies on economic growth: the spatial organization of the economy in regions. For that purpose, the empirical analysis has used spatial economic tools, applied to a panel model with fixed effects and SAR (1) errors. The findings show the absence of trends towards conditional convergence, which means that the Peruvian Departments as such lack steady growth paths in the medium term. The data also show that during the hyperinflation and structural adjustment periods, the less developed Departments presented slow down factors. Finally, the analysis shows that the public expenditure plays an important compensatory role of the decelerating and accelerating forces of growth, and that its impact is more favorable to growth when regions are considered, instead of the Departments. These results reinforce the idea that integration of the Departments into regions is necessary.