The Mir station has been in a 51.65 deg inclination orbit since March 1986. In March 1995, the first US astronaut flew on the Mir-18 mission and returned on the Space Shuttle in July 1995. Since then three additional US astronauts have stayed on orbit for up to 6 months. Since the return of the first US astronaut, both the Spektr and Priroda modules have docked with Mir station, altering the mass shielding distribution. Radiation measurements, including the direct comparison of US and Russian absorbed dose rates in the Base Block of the Mir station, were made during the Mir-18 and -19 missions. There is a significant variation of dose rates across the core module; the six locations sampled showed a variation of a factor of nearly two. A tissue equivalent proportional counter (TEPC) measured a total absorbed dose rate of 300 mu Gy/day, roughly equally divided between the rate due to trapped protons from the South Atlantic Anomaly (SAA) and galactic cosmic radiation (GCR). This dose rate is about a factor of two lower than the rate measured by the thinly shielded (0.5 g cm^-2 of Al) operational ion chamber (R-16), and about 3/2 of the rate of the more heavily shielded (3.5 g cm^-2 of Al) ion chamber. This is due to the differences in the mass shielding properties at the location of these detectors. A comparison of integral linear energy transfer (LET) spectra measured by TEPC and plastic nuclear track detectors (PNTDs) deployed side by side are in remarkable agreement in the LET region of 15 -1000 keV/mum, where the PNTDs are fully efficient. The average quality factor, using the ICRP-26 definition, was 2.6, which is higher than normally used. There is excellent agreement between the measured GCR dose rate and model calculations, but this is not true for trapped protons. The measured Mir-18 crew skin dose equivalent rate was 1133 muSv/day. Using the skin dose rate and anatomical models, we have estimated the blood-forming organ (BFO) dose rate and the maximum stay time in orbit for International Space Station crew members.