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The novelties offered by using a composite right/left-handed (CRLH) waveguide as the feeding structure of a slot array antenna are surveyed for some common slot arrangements. Furthermore, a complete approach to the design of beam-steerable arrays using the CRLH waveguide technology and meeting a set of specific requirements is presented. To illustrate the proposed methodology, a 13-slot array antenna has been designed, built and measured. It provides a full-space beam scanning from - 40° to +30° as the frequency changes over a 25% bandwidth with a good input match, narrow beamwidth, moderate side-lobe performance and acceptable gain values.