[Authors] O. I. Reinov [Title] Some remarks on spectra of nuclear operators [AMS Subj-class] 47B10 Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.) [Abstract] We give criteria for the spectra of some nuclear operators in subspaces of quotients of L_p-spaces to be central-symmetric, as well as for the spectra of linear operators in Banach spaces to be Z_d-symmetric in the sense of B. Mityagin. Also, we present a short proof of a generalization of Mityagin's theorem. [Comments] LaTeX, English, 9 pp. [Contact e-mail] orein51@mail.ru