Experimental autoimmune encephalomyelitis (EAE) is a procedure used in the laboratory to examine drugs that may have utility in treating multiple sclerosis (MS). The problem of modeling the disease curve in animals with EAE is studied. The classification of animals after each experiment is considered and the chi-square test is proposed to test a homogeneity between treatment groups. A mixture type of nonlinear mixed-effects model with repeated measurements is considered, assuming that the onset and/or remission of disease is the fixed effect as well as the random effect. Statistical inference on the parameters of the disease curves is discussed. The proposed model is shown to be efficient for comparing the disease curves with different treatments. Examples concerning the study of the effects of test compounds in EAE are presented to illustrate the proposed model and statistical methodologies.