We present the spatially accelerating solutions of the Maxwell equations. Such nonparaxial beams accelerate in a circular trajectory, thus generalizing the concept of Airy beams.For both TE and TM polarizations, the beams exhibit shape-preserving bending with subwavelength features, and the Poynting vector of the main lobe displays a turn of more than 90°.We show that these accelerating beams are self-healing, analyze their properties, and compare to the paraxial Airy beams. Finally, we present the new family of periodic accelerating beams which can be constructed from our solutions.

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