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The propagation behavior and M2-factor of truncated cosh-Gaussian (ChG) beams are studied by using the asymptotic approach. Detailed numerical results are given to illustrate the dependence of M2-factor on the beam decentered parameter β, truncation fraction p and power fraction f. Our results are self-consistent and reduce to those of Pare and Belanger [Opt. Commun.123, p. 679 (1996a); Proc. SPIE2870, p. 104 (1996b)]. The advantage of the approach is shown, and the problems introduced by the hard-aperture diffraction and the approach used are discussed.