The C14 Laves phase Fe2Ti is stable in an extended compositional range. Within this range Fe2+xTi1-x orders ferromagnetically for x >0 and anti ferromagnetically for x less than or equal to0 [1]. Consequently, slight changes in stoichiometry strongly alter the magnetic state about x approximate to0. Thin films showing (110)- and (001)-texture, depending on stoichiometry, have been prepared using MBE deposition techniques. SQUID-magnetization measurements at various temperatures and magnetic fields have been performed. Temperature dependent measurements reveal ferromagnetism at elevated temperatures. Antiferromagnetic contributions are discernible below approximately 140 K. Consequently, the temperature dependence of the magnetization deviates from Bloch-like behavior at low temperatures reminiscent of results obtained for bulk samples [2]. Magnetic hysteresis loops taken after field-cooling are shifted significantly in opposite direction of the cooling field giving evidence for strong induced unidirectional anisotropy. Temperature increase causes the effect to gradually disappear above the antiferromagnetic ordering temperature. We suggest that exchange coupling effects at the interfaces of ferromagnetic and antiferromagnetic ordered Fe2Ti regions cause this exchange bias effect, which is well known from other materials.