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Current approaches for modeling electromechanical systems (EMS) are either based on deriving the system equations by applying a single formulation to all problem domains, or they are based on trying to integrate different software packages/modules to solve the interdisciplinary problem. In this paper, we present a component-based approach that is suitable for hybrid electromechanical systems. This approach allows the governing equations of each component to be defined in terms of its natural variables. The different component equations are then brought together to form a single system of differential-algebraic equations (DAE's), which can be numerically solved to obtain the system response. The formulation includes monitor functions which can be used to detect when a qualitative system change has occurred, and to switch to a new set of governing equations to reflect this change. To handle discrete devices, the approach takes advantage of the fact that even such devices generally display piecewise smooth behavior, i.e., in the interval between successive sampling/switching times, they usually act as continuous devices. A single step integrator is used to integrate the system response interval by interval, without stepping over a sampling/switching time during an integration time step. The integration is restarted at each sampling/switching time. There is considerable flexibility in how the components can be defined. Examples of mechanical and electrical components are presented, and two numerical examples are solved to illustrate the efficacy of the proposed method. One example is a link that is driven by a DC motor through a gearbox. The results of this example were verified against Simulink, and good agreement was observed. The second example is a hybrid system that uses encoder feedback to control velocity of a dc motor driven link.