In this paper, we establish new Lyapunov-type inequalities for two classes of one-dimensional quasilinear elliptic systems of resonant type, which improve the recent results of Tang and He [X. H. Tang, X. He, Lower bounds for generalized eigenvalues of the quasilinear systems, J. Math. Anal. Appl. 385 (2012) 72-85] when 1 < p(i) < 2 for i = 1,2, ..., n. (C) 2011 Elsevier Inc. All rights reserved.