In this paper, we will compare and evaluate the various noise cancellation schemes available in what we will term the 'dual microphone systems' (DMS). A DMS is a directional audio-capturing device consisting of two microphones with possibly different directional characteristics: omnidirectional, bidirectional or cardioid. A general structure is proposed to coherently represent the different schemes for the DMS. This is followed by a theoretical derivation of performance of various DMS configurations under incoherent, coherent and diffuse noise fields. The relationships between the different configurations and some guidelines for design of DMS are also presented.