Free electron lasers with transverse synchronizing magnetic fields are considered. A constant transverse magnetic field or one with a constant longitudinal gradient makes it possible to maintain the resonance longitudinal velocity of an electron while changing its transverse velocity. The process of wave amplification in a FEL with a synchronizing magnetic field is investigated analytically and numerically. Two possible amplification regimes are considered: electron capture by the ponderomotive wave and reflection of particles by the ponderomotive potential. An expression for the gain in the small-signal regime is obtained. Comparison with other schemes of synchronized FELS is made. The self-consistent equations describing wave amplification are solved. An analysis is made of the possibility to enhance the efficiency of a FEL with a longitudinal magnetic field by a reduction of the nonisochronism parameter of the electron oscillations in a wave field.