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A linear array of surface-wave launchers (SWLs) is presented for surface-wave (SW) beam steering on a grounded dielectric slab (GDS). Specifically, a two-element array of directive Yagi-Uda like SWL antennas (operating between 21-24 GHz) is investigated. By varying the relative phase difference between SWL elements, the excited SW field distribution can be steered. In addition, a six-element linear array of SWLs with nonuniform weighting is also presented. If metallic gratings are placed on top of the GDS, the bound SW mode can be transformed into a radiated leaky-wave (LW) mode and directive beam patterns can be generated in the far field. A specific elliptical grating configuration is also investigated demonstrating single frequency cylindrical-sector LW beam steering. These slotted SWL arrays can be useful for novel SW beam scanning designs, millimeter wave power distribution systems and new LW antennas.