Abstarct: In some semiparametric survival models which are useful and flexible to analyze recurrent event data, some coefficients are dependent to time. In these models, estimators of the coefficients do not exist in closed forms. Therefore, we have to estimate them by using numerical methods. Due to complicated forms of such estimators, it is too hard to know their sampling distributions. In such cases, statisticians usually use the asymptotic theory to evaluate properties of the estimators. In this thesis, we first introduce the model and propose a method, by using the Taylor expansion and kernel methods, to fit the model. Then, we establish the consistency and asymptotic normality of estimators. After that, we evaluate the performance of model and estimating procedure by a heavy simulation study. Finally, we apply the modeling approach on a real data set on heart disease patients in one of the Mashhad hospitals.