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Penrose limits are considered in space-times admitting two abelian,space-like Killing vectors in vacuum as well as in the presence of anelectromagnetic field. This type of space-times describe inhomogeneouscosmologies as well as colliding plane gravitational and electromagnetic waves.Following the work of Tod [1] the conditions for diagonal Penrose limits areinvestigated in these backgrounds. The twistor equation is considered in thesespace-times and solutions given in the Penrose limit.

Penrose limits of inhomogeneous space-times, their diagonalizability and twistors