The aim of this work is to construct nonseparable, stationary covariance functions for processes that vary continuously in space and time. Stochastic modelling of phenomena over space and time is important in many areas of application. But choice of an appropriate model can be difficult as we need to ensure that we use valid covariance structures. A common choice for the process is a product of purely spatial and temporal random processes. In this case, the resulting process possesses a separable covariance function. Although these models are guaranteed to be valid, they are severely limited, since they do not allow space-time interactions. We propose a general and flexible class of valid nonseparable covariance functions through mixing over separable models. The proposed model allows for different degrees of smoothness across space and time and long-range dependence in time. Moreover, the proposed class has as particular cases several popular covariance models proposed in the literature such as the Matérn and the Cauchy Class. We use a Markov chain Monte Carlo sampler for Bayesian inference and apply our modelling approach to the Irish wind data.