We have used time-resolved spectroscopy to measure the relaxation of spin polarizations in the narrow gap semiconductor material n-InAs as a function of temperature, doping, and pump wavelength. The results are consistent with the D'Yakonov-Perel mechanism for temperatures between 77 and 300 K. However, the data suggest that electron-electron scattering should be taken into account in determining the dependence of the spin lifetime on the carrier concentration in the range 5.2x10(16)-8.8x10(17) cm(-3). For a sample with doping of 1.22x10(17) cm(-3) the spin lifetime was 24 ps at room temperature. By applying a magnetic field in the sample plane we also observed coherent precession of the spins in the time domain, with a g factor g(*)=-13, also at room temperature.