A theory of continuous dissipative media with topological defects is presented. We propose a reduction of information contained in the original nonlinear field equation which will describe long time and large scale behaviors of the system. The result is a coupled set of equations of motion for topological defects and phase variables away from the defects, which generalizes the phase dynamics. The theory is illustrated for the Darcy-Rayleigh convection. A gauge-theoretical approach to deal with continuous distribution of topological defects is described. Possible relevance of our approach to evolution of random patterns is suggested.