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We consider type IIB string in the two plane-wave backgrounds which may beinterpreted as special limits of the AdS_3 x S^3 metric supported by either theNS-NS or R-R 3-form field. The NS-NS plane-wave string model is equivalent to adirect generalization of the Nappi-Witten model, with its spectrum beingsimilar to that of strings in constant magnetic field. The R-R model can besolved in the light-cone gauge, where the Green-Schwarz action describes 4massive and 4 massless copies of free bosons and fermions. We find the spectraof the two string models and study the asymptotic density of states. We alsodiscuss a more general class of exactly solvable plane-wave models with reducedsupersymmetry which is obtained by adding twists in two spatial 2-planes.Comment: 36 pages, harvmac. v2: discussion of equivalence of the supergravity  parts of the spectra of the NS-NS and R-R models added in sect.5.3; v3: added  remark on periodicity of the NS-NS spectrum; v4: minor correction in sect.6.

On solvable models of type IIB superstring in NS-NS and R-R plane wave backgrounds