The space-time asymptotic analysis in lossless dispersive media for noncollimated pulsed wave objects with real spectra, as performed in Part I is here extended to the complex frequency and wavenumber spectra that characterize pulsed beam (PB) wave packets. To address the problem systematically, all spectral components in the formal asymptotic wave number frequency synthesis are expanded to second order away from the beam axis, which represents a real space-time ray with real spectra. Off-axis observation points in the paraxial region are reached by complex space-time rays with complex spectra. The complex off-axis spectra lead to corrections of the real on-axis spectra, in addition to introducing an imaginary (evanescent) decay component. Efforts are in progress to assess the wave physics that accompany these results, and to determine the modifications, due to dispersion, of the highly resolved PB in a nondispersive environment. Synthesizing PB profiles for focusing at a given space--time point in the dispersive medium are also considered.