Among cosmic rays, the heavy nuclei ( HZE particles) like iron provide the dominant contribution to the dose equivalent during exposures in space. The LET distributions and radiation doses of cosmic-ray components have been calculated--with and without the quality factors--for a set of shielding and tissue self-shielding penetration depths. The relative contributions of heavy ions among solar flare particles to the dose equivalent are also explored. The transport calculations of the nuclei in air, shielding materials, and biological tissue-like material were carried out using the partial and total nuclear cross-section equations and nuclear propagation codes of Silberberg and Tsao . Outside the magnetosphere , at solar minimum, the product of the unshielded dose and the quality factors of cosmic-ray protons and heavy nuclei with atomic number Z greater than or equal to 6 are about 5 and 47 rem/year, respectively. With 4 g/cm2 aluminum shielding and at a depth of 5 cm in a biological phantom of 30 cm diameter, the respective values of the dose equivalents are about 4 and 11 rem/year. Due to the hard spectrum of cosmic rays, the attenuation of protons thus is relatively modest, while that of heavy nuclei is larger due to the larger interaction cross section. The dose equivalent of neutrons in the shielded case mentioned above is similar to that of protons. The biological risks are tentatively assessed in terms of the BEIR 1980 report. Uncertainties in risks due to possible large RBE values at low doses of high-LET radiation and due to the microbeam nature of damage by heavy ions are pointed out. Certain experiments and studies by radiobiologists are suggested for reducing the uncertainties in the estimates of the risks.