We used mathematical models to assess the importance of strategies of growth and life history for the competition between clonal plant species. We studied two abstract clonal species representing the "phalanx" and "guerilla" strategies where phalanx plants have modules with longer life spans, higher birth rates, and shorter distances between parent and vegetative offspring than guerilla plants. Because seedling recruitment is rare in many clonal plants we only considered vegetative reproduction. We included architectural elements in a cellular, spatially explicit simulation model. To identify biological determinants of the simulation results we used analytical difference-equation models. We investigated interspecific competition in both the r-and K-phases of population development in a homogeneous environment. Without module interactions (r-phase) initial growth rate λ was essentially determined by the difference between the rates of module production and mortality and modified by the development rate of juvenile modules. With interactions (K-phase), long-term coexistence or exclusion of species was determined by competitiveness C. This measure was defined by the quotient of the rates of module production and mortality (= mean life-time module production per module), multiplied by a factor describing juvenile survival, and two spatial correction factors. These two correction factors accounted for limited dispersal distance, variation in branching angles, and plastic search behaviour of juvenile modules. Non-random initial species distributions changed the rate but not the final outcome of species exclusion. The guerilla plant had a higher initial population growth rate whereas the phalanx plant was superior in densely populated habitats. Imposing spatially heterogeneous disturbances by density-independent mortality led to a mixture of densely and sparsely populated patches. This favoured the guerilla strategy because it allowed the modules to rapidly colonize gaps and to make better use of available space. Our model results correspond well with empirical findings. Long-term competition in homogeneous environments was ruled by life-history parameters, and spacer length played an additional important role in the transition from low to high densities and under disturbance. Thus, when comparing guerilla and phalanx plants growth strategy in a narrow sense must be clearly distinguished from the whole complex of life history and growth. Future inclusion of sexual reproduction into our complementary models may allow examination of fitness of clonal plants in a community.