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In this paper, we investigate the evolution characteristics of periodically revived elliptical cos-Gaussian solitons and breathers based on nonlocal nonlinear Schrödinger equation, which can be applied into describing the beam evolution in nonlocal nonlinear media. The elliptical cos-Gaussian solitons can present a variety of intensity distribution modes. With different incident energies, the statistical spot size can remain unchanged during the process of evolution, namely the soliton state; otherwise, the statistical spot size changes periodically, namely the breathing state. The transverse intensity mode always changes periodically which is similar to the higher-order temporal solitons. That is, they can be revived to the original mode at the end of each evolution period. Mathematical expressions are derived to describe the soliton propagation, the intensity pattern, the statistical spot size and the axial intensity etc. Various evolution characteristics are discussed in details and illustrated by numerical simulations.