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A novel application of leaky-wave antennas (LWAs) as integrated antennas and multiplexers/demultiplexers is proposed and experimentally demonstrated in the millimeter-wave band at 60~GHz. The first application is demultiplexing of an oblique-incident free-space wideband plane wave into $2N$ channels using $N$ LWAs with different beam-scanning laws. The second application is $N$--channel multiplexing and demultiplexing using $N$ pairs of identical LWAs in each other's far-field, where each LWA pair is designed such that the broadside frequency is the center frequency of its respective channel. Friis transmission equation is used to analytically demonstrate the two proposed applications using Gaussian radiation beams. The LWAs are then implemented using reflection-cancelling slot pairs using substrate integrated waveguide (SIW) technology. Full-wave simulations are used to demonstrate the first application by demultiplexing an incident plane wave into two and four channels using two LWAs. Finally, the two proposed applications are experimentally demonstrated by conducting horn-to-LWA and LWA-to-LWA transmission measurements and successfully showing broadband frequency discrimination. The proposed LWAs provide a simple, compact, high-efficiency, and low-profile multiplexing/demultiplexing solution with high-integration capability with other circuitry. Compared to conventional multiplexers, the proposed solution does not require matching networks and can be directly scaled to higher frequencies using the same architecture.