This thesis examines the size-growth relationship for banking and manufacturing firms. In particular it tests the Law of Proportionate Effect (LPE) which suggests that there is no relationship between firm size and growth. Tests of the LPE are carried out for eight European banking markets (Belgium, Denmark, France, Germany, Italy, Netherlands, Spain and the United Kingdom) and for three bank types (commercial, co-operative and savings) over the period 1990 to 1994. Employing three measures of size (total assets, equity and off balance sheet business) models are estimated that test for size effects on growth, and the influences of previous growth, bank type and country membership. In the majority of cases, bank growth is independent of bank size, so the LPE holds. However, small banks grew faster than their larger counterparts (in terms of assets and equity) in France, Italy and Spain. The LPE is also investigated for a sample of European manufacturing firms drawn from five countries and eleven industry groups. In contrast to the banking industry there is less evidence that the LPE holds. In most cases small firms grew proportionately faster than their larger counterparts. Using stochastic simulation techniques, the effects of firm growth, entry, exit and merger activity on the evolution of bank sizes and market concentration is examined. Using a simulated industry in which the LPE holds as the benchmark, the implications of various alternative assumptions regarding bank growth were examined. Superimposition of entry leads to a lower mean bank size and lower levels of concentration. Exit leads to higher mean bank size and increased concentration. Mergers lead to increases in mean bank size and concentration in all simulated industries. Using the simulations methodology, hypothetical projections as to the future structure of the banking markets in France, Germany, Italy, Spain and the UK are carried out. Overall, the simulations suggest that bank numbers are likely to decrease in all countries. The market shares of the largest banks are also projected to decline in all countries with the exception of the UK.