Recurrent event data arise frequently from medical research. Examples include repeated infections, recurrence of tumors, relapse of leukemia, repeated hospitalizations, recurrence of symptoms of a disease, and so on. In the analysis of recurrent event data, the proportional rates model assumes that the regression coefficients are time invariant. In reality, however, these parameters may vary over time, and the temporal covariate effects on the event process are of great interest. In this article, we formulate a class of semiparametric marginal rates models, which incorporate a mixture of time-varying and time-independent parameters, to analyze recurrent event data. For statistical inference on model parameters, an estimation procedure is developed and asymptotic properties of the proposed estimators are established. In addition, we develop tests for investigating whether or not covariate effects vary with time. The finite-sample behaviors of the proposed methods are examined in simulation studies. An example of application of the proposed methodology is illustrated on a set of data from a clinic study on chronic granulomatous disease.