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The exponential Euler method has recently shown great promise as a numerical method for solving large, sparse systems of differential equations. Particularly attractive is the method's excellent performance in the absence of preconditioning - a feature that gives it a significant advantage over other methods when it comes to parallelisation. However, the method has not yet been satisfactorily extended to handle systems of differential/algebraic equations. This precludes the method from being applied to many important problems - particularly systems arising from the method of lines applied to certain partial differential equations. This project would involve an investigation of some extensions that have been previously proposed for handling these DAE systems, with a view to improving upon these ideas and thus advancing the state of the art in this field.