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We construct the partition function of 1/8 BPS dyons in type II string theoryon T^6 from counting of microstates of a D1-D5 system in Taub-NUT space. Ouranalysis extends the earlier ones by Shih, Strominger and Yin and by Pioline bytaking into account the walls of marginal stability on which a 1/8 BPS dyon candecay into a pair of half-BPS dyons. Across these walls the dyon spectrumchanges discontinuously, and as a result the spectrum is not manifestlyinvariant under S-duality transformation of the charges. However the partitionfunction is manifestly S-duality invariant and takes the same form in alldomains of the moduli space separated by walls of marginal stability, -- thespectra in different domains being obtained by choosing different integrationcontours along which we carry out the Fourier transform of the partitionfunction. The jump in the spectrum across a wall of marginal stability,calculated from the behaviour of the partition function at an appropriate pole,reproduces the expected wall crossing formula.

N=8 Dyon Partition Function and Walls of Marginal Stability