************************************************************************* 52074 We propose a 40-ks ASCA observation of G 359.2-0.8, an axisymmetric radio nebula referred to as ``The Mouse''. This unusual nebula is one of the several axisymmetric radio sources discovered during the mid- 1980s. Their physical nature is a mystery. It has been proposed that such nebulae are the work of relativistic outflows from either a fast moving pulsar or a moving binary system. An ASCA observation of the spectrum and time series analysis of the Mouse would make it possible to distinguish between these models and contribute greatly to the resolution of this decade old mystery. *************************************************************************