We use dynamical equations to represent and analyse the slash and burn agriculture. The slash and burn agriculture is a production system that is broadly diffused among the peasants who inhabit the low lands of Bolivia. The study of this production system is important because it has an unfavorable impact on the farm economy as well as on the environment. Nevertheless, it may represent only the first stage towards sustainable forms of production. We find that, under certain conditions, the farm can reach a stable equilibrium. The equilibrium can be reached following three different kinds of paths, corresponding to three local forms of convergence for the economy. We associate a slow evolution of the farm with an equilibrium, corresponding to two real eigen-values in the matrix of the linearized dynamic system; a moderate evolution with another equilibrium, corresponding to one eigen-value; and an evolution with fluctuations to a third equilibrium, associated with two complexes and conjugated eigen-values. Keywords: Developing countries; Agriculture of colonization; Dynamic models JEL classification: Q1