  We show that new families of accelerating and almost nondiffracting beams
(solutions) for Maxwell's equations can be constructed. These are complex
geometrical optics (CGO) solutions to Maxwell's equations with nonlinear
limiting Carleman weights. They have the form of wave packets that propagate
along circular trajectories while almost preserving a transverse intensity
profile. We also show similar waves constructed using the approach combining
CGO solutions and the Kelvin transform.
