The absorption and transport scattering coefficients of caucasian and negroid dermis, subdermal fat and muscle have been measured for all wavelengths between 620 and 1000 nm. Samples of tissue 2 mm thick were measured ex vivo to determine their reflectance and transmittance. A Monte Carlo model of the measurement system and light transport in tissue was then used to recover the optical coefficients. The sample reflectance and transmittance were measured using a single integrating sphere `comparison' method. This has the advantage over conventional double-sphere techniques in that no corrections are required for sphere properties, and so measurements sufficiently accurate to recover the absorption coefficient reliably could be made. The optical properties of caucasian dermis were found to be approximately twice those of the underlying fat layer. At 633 nm, the mean optical properties over 12 samples were and for absorption coefficient and and for transport scattering coefficient for caucasian dermis and the underlying fat layer respectively. The transport scattering coefficient for all biological samples showed a monotonic decrease with increasing wavelength. The method was calibrated using solid tissue phantoms and by comparison with a temporally resolved technique.