The existence of stars and galaxies reqires cosmological models with aninhomogeneous matter and radiation distribution. But in these models theinitial singularity surface t_0(r) is in general homogeneous (independent ofr). In this second paper of a series devoted to an inhomogeneous Big Bangsingularity, we investigate the cosmic microwave background radiation (CMBR)dipole. A special Tolman-Bondi Universe is used to study the effect of aBig-Bang singularity, depending linearly on r, on the CMBR anisotropy. It isshown that, for an observer located off the ``center'' of this Universe (r=0),the parameters of the model can be tuned so as to reproduce, with a goodapproximation, the dipole and the quadrupole moments of the CMBR anisotropyobserved in recent experiments. If the dipole should prove cosmological, aslight delaying of the Big-Bang over spatial coordinates would thus be a goodcandidate for its interpretation.
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