We study the electron spin relaxation in both symmetric and asymmetric GaAs/AlGaAs quantum wells (QWs) grown on (110) substrates in an external magnetic field B applied along the QW normal. The spin polarization is induced by circularly polarized light and is detected using the time-resolved Kerr rotation technique. In the asymmetric structure, where a δ-doped layer on one side of the QW produces the Rashba contribution to the conduction-band spin–orbit splitting, the lifetime of electron spins aligned along the growth axis exhibits an anomalous dependence on B in the range 0 < B < 0.5 T; this results from the interplay between the Dresselhaus and Rashba effective fields which are perpendicular to each other. For larger magnetic fields, the spin lifetime increases, which is a consequence of the cyclotron motion of the electrons and is also observed in (001)-grown quantum wells. The experimental results are in agreement with the calculation of the spin lifetimes in (110)-grown asymmetric quantum wells described by the point group Cs, where the growth direction is not the principal axis of the spin-relaxation-rate tensor.