Electron spin relaxation times have been measured in InSb and InAs epilayers in a moderate (<4 T) external magnetic field. A strong and opposite field dependence of the spin lifetime was observed for longitudinal (Faraday) and transverse (Voigt) configuration. In the Faraday configuration the spin lifetime increases because the D'yakonov-Perel' dephasing process is suppressed. At the high field limit the Elliot-Yafet spin flip relaxation process dominates, enabling its direct determination. Conversely, as predicted theoretically for narrow band gap semiconductors, an additional efficient spin dephasing mechanism dominates in the Voigt configuration significantly decreasing the electron spin lifetime with increasing field. © 2010 American Institute of Physics.