The urgency of the discussed issue is caused by the need to resolve the problems in structural and parametric identification of phenomenological models in oil and gas production. The main aim of the study is to develop models and algorithms for adaptive identification in evolutionary processes of oil and gas production based on integrated systems of phenomenological models with variable time-dependent parameters. The methods used in the study are: the theoretical and practical developments in the monitoring and management of oil and gas production, system analysis, system identification with additional a priori information, optimization of functions and linear algebra. The problems in structural and parametric identification were solved theoretically based on integrated systems of phenomenological models and experimentally based on field data of oil annual output field in Tomsk region. The results: The authors proposed to use the integrated systems of phenomenological models based on a priori information with variable time-dependent parameters in order to solve problems of identification in evolutionary process of oil and gas production. They proposed and investigated algorithms of adaptive identification in evolutionary processes of oil and gas production on the basis of solving optimization problems under conditions of a priori nonparametric uncertainty, when the parameters of the integrated systems of phenomenological models are presented by unknown unambiguous time functions. It was shown as well that the inclusion of a priori information can improve significantly the accuracy in estimating forecast production and recoverable reserves.