Previous research on estimation of the progression of chronic disease, from the normal preclinical screen-detectable phase (PCDP) to the final clinical phase, has usually assumed constant transition rates and has rarely addressed how relevant covariates affect multi-state transitions. The present study proposes two non-homogeneous models using the Weibull distribution and piecewise exponential model, together with covariate functions of the proportional hazard form, to tackle these problems. We illustrate the models by application to a selective breast cancer screening programme. The results of the Weibull model yield estimates of scale and shape parameters for annual preclinical incidence rate as 0.0000058 (SE=0.0000019) and 2.4755 (SE=0.1153), the latter being significantly higher than 1. Annual transition rate was estimated as 0.3153 (SE=0.1385). Relative risks for the effects of late age at first pregnancy (AP) and high body mass index (BMI) on preclinical incidence rate were 1.98 and 2.59, respectively. The corresponding figures on the transition from the PCDP to clinical phase were 1.56 and 1.99, respectively. Non-homogeneous Markov models proposed in this study can be easily applied to rates of progression of chronic disease with increasing or decreasing rates with time and to model the effect of relevant covariates on multi-state transition rates. Copyright © 2002 John Wiley & Sons, Ltd.