In this work we study the inflammatory process resulting in the development ofatherosclerosis. We develop a one- and two-dimensional models based on reaction-diffusionsystems to describe the set up of a chronic inflammatory response in the intima of anartery vessel wall. The concentration of the oxidized low density lipoproteins (ox-LDL) inthe intima is the critical parameter of the model. Low ox-LDL concentrations do not leadto a chronic inflammatory reaction. Intermediate ox-LDL concentrations correspond to abistable system and can lead to a travelling wave propagation corresponding to a chronicinflammatory reaction. In this case the disease development depends on the initialcondition. If the concentration of monocytes in the intima is sufficiently high, which can becaused by an inflammation related to other factors, then the development of atherosclerosiscan start. Otherwise, the system returns to the stable disease free equilibrium. Highox-LDL concentrations correspond to a monostable system and even a small perturbationof the non inflammatory case leads to a travelling wave propagation which corresponds to achronic inflammatory response.