Specific resistance loci in plants are generally very efficient in controlling development of pathogen populations. However, because of the strong selection pressure exerted, these resistances are often not durable. The probability of a resistance breakdown in a pathosystem depends on the evolutionary potential of the pathogen which is affected by: (i) the type of resistance (monogenic and/or polygenic), (ii) the type of reproduction of the pathogen (sexual and/or asexual), (iii) the capacity of the pathogen for dispersal, (iv) the resistance deployment strategy (pyramiding of specific resistances, mixture of cultivars, spatio-temporal alternation), (v) the size of the pathogen population, which is affected by control methods and environmental conditions. We propose the concept of Integrated Avirulence Management (IAM) to enhance the durability of specific resistances. IAM involves a strategy to limit the selection pressure exerted on pathogen populations and, at the same time, reduce the size of pathogen populations by combining cultural, physical, biological or chemical methods of control. Several breakdowns of resistance specific to Leptosphaeria maculans, the causal agent of phoma stem canker have occurred in Europe and in Australia. This review paper examines control methods to limit the size of L. maculans populations and discusses how this limitation of population size can enhance the durability of specific resistances. It proposes pathways for the development of a spatially explicit model to define IAM strategies. Simulation results are presented to demonstrate the potential uses of such a model for the oilseed rape/L. maculans pathosystem.