Transmit-array design is more challenging for dual-band operation than for single-band, due to the independent 360º phase wrapping jumps needed at each band when large electrical length compensation is involved. This happens when aiming at large gains, typically above 25 dBi with beam scanning and F/D≤1. No such designs have been reported in the literature. A general method is presented here to reduce the complexity of dual-band transmit-arrays design, valid for arbitrarily large phase error compensation and any band ratio, using a finite number of different unit-cells. The procedure is demonstrated for two off-set transmit-array implementations operating in circular polarization at 20 GHz(Rx) and 30 GHz(Tx) for Ka-band satellite-on-the-move terminals with mechanical beam steering. An appropriate set of 30 dual-band unit-cells is developed with transmission coefficient >‒0.9 dB. The full-size transmit-array is characterized by full-wave simulation enabling elevation beam scanning over 0-50º with gains reaching 26 dBi at 20 GHz and 29 dBi at 30 GHz. A smaller prototype was fabricated and measured, showing a measured gain of 24 dBi at 20 GHz and 27 dBi at 30 GHz. In both cases the beam pointing direction is coincident over the two frequency bands, thus confirming the proposed design procedure.