Let A=(a0,a1,...,ak) denote a finite collection of ordered transient states traversed by an individual on study for a specific period of time. In medical studies, the initial state a0 often corresponds to an initial disease-free state, while states ar (r =1, 2,…,k) would represent repeated non-fatal events of the same type (see, MacKenzie (1997), “On a non-proportional hazards regression model for repeated medical random counts”, Statistics in Medicine, 16, 1831-1843).Associated with the states ar (r =1, 2, …,k) are the times Tr (random variables) at which transitions occur from states ar−1 to ar so that the underlying stochastic process may be described by (a0,T1,a1,T2,…), overall. Let the hazard for the r-th event be modeled byλr(tr|xr)= λ0(tr)h(tr,xr),where λ0(tr) is some baseline hazard function, xr is a vector of covariates measured at baseline and at each subsequent event (r≥1), and h(tr, xr) is some link function associating the covariates to the hazard function, which itself may be assumed to involve tr or not.There are two approaches one could take in order to estimate the above model: either to take the baseline hazard function in a specific parametric form (for example, to be Weibull, lognormal, etc.) or to take it in a nonparametric form (for example, as a stepwise constant form, etc.) and develop the corresponding statistical analysis based on maximum likelihood estimation. Additionally, there are many choices of the link function that one could make, such as a log-linear link function (like in a Cox’s proportional hazards model). General point estimation, interval estimations and tests of hypotheses based on the likelihood criterion will be of interest to develop and this will be the primary aim of the project. In addition, validity methods of the use of such a model for given data will be developed as well. Data sets will then be used to illustrate the methods developed and asses their efficiency.