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A new approach for determining the Doppler spectrum of narrowband multipath channels by assuming a three-dimensional propagation model is proposed. The new derivation methodology is first applied to determine the Doppler spectrum of a Rayleigh channel, when an omni-directional mobile-terminal antenna is assumed. The obtained results are shown to agree with the existing analytical results, which are available for particular assumptions regarding the angular distribution of the received multipath power. The main contribution is the derivation of the Doppler spectrum of the mobile satellite channel, where directive tracking terminal antennas are assumed. The results, which are dependent on the antenna's beamwidth and bearing, apply to emerging types of commercial vehicular satellite systems.