We consider parameter estimation based an iid sequence of censored observations of a finite state modulated renewal process. Its intensities assume a similar form as in Cox regression except that the baseline intensities are functions of the backwards recurrence time of the process while the covariates may depend on both calendar and duration time clock. Under conditions slightly stronger than in Andersen and gill we show that if the covariates depend on the backwards recurrence time only then the parameter estimates have the same asymptotic distribution as in the classical Cox regression. The choice of time independent covariates corresponds to Markov renewal processes. In this special case we discuss estimation of the renewal and transition probability matrices and show weak consistency of the bootstrap.