EUVE and ROSAT observations of Comet Hyakutake revealed emission of 7 x 10(24) photons per second in the soft Xray, We discuss and develop methods to calculate production of soft X-ray photons in cometary dust and gas by the following processes: (1) scattering and (2) fluorescence of solar X-rays; (3) K- and L-shell ionization by solar-wind protons and (4) electrons, and (5) by high-energy cometary ions; (6) bremsstrahlung of solar-wind electrons; (7) cometary magnetospheric substorms; (8) collisions between cometary and interplanetary dust particles; (9) scattering, fluorescence, and bremsstrahlung by very small particles with mass on the order of 10(-19) g; and (10) charge transfer of the solar-wind heavy ions with cometary molecules suggested by T. E. Cravens (1997, Geophys. Res. Lett. 24, 105-108). Very small attogram particles were detected in Comet Halley by N. G. Utterback and J. Kissel (1990, Astron. J. 100, 1315-1322) using the PUMA and PIA dust analyzers from the Vega and Giotto spacecraft. Of all these processes, only scattering by very small particles and charge transfer of the solar-wind heavy ions are capable of producing the measured soft X-ray emission. Ln the case of very small particles, the mean particle mass of 4.6 x 10(-19) g suggested by Utterback and Kissel implies that the total production of these particles, which exceeds that of gas by a factor 3.6 (in mass), is inconsistent with the polarization and color of Comet Halley, Both polarization and color require a reduction of the mean mass to (1-2) x 10(-19) g. This reduction strongly affects the visible brightness of the par-tides, which is proportional to m(2), with a relatively weak effect on the soft X-ray emission. We calculate the charge transfer process using the solar-wind ion densities and velocities in comet from both the model of T. I. Gombosi et al. (1994, J. Geophys. Res. 99, 21,525-21,539) and the Giotto measurements of Lu-particles and. Hei ions in Comet Halley. The calculated emission constitutes 20-35% of the measured value. X-ray spectroscopy of the observed emission, spectroscopy of the He+ 304 Angstrom and He 522 Angstrom lines, and UV spectroscopy of cometary dust down to 1800 Angstrom may help in determining the contributions of the above processes. (C) 1997 Academic Press.