We propose frailty regression models in mixture distributions assuming the distribution of frailty to be a gamma distribution. We consider Weibull mixture as an example. There are some interesting situations like survival times in genetic epidemiology, dental implants of patients and twin births (both monozygotic and dizygotic) where genetic behavior (which is unknown and random) of patients follows a known frailty distribution. These are the situations, which motivate to study this particular model.