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In this paper, two necessary and sufficient conditions, and asufficient condition of A (a)-acceptability for (n,m) rational approximation to function exp(z) are given, where a∈ (0, π/2). A necessary and sufficient condition of A-acceptability for (n,m) rational approximation to exp(z) of order p is obtained, where n≤m≤p.CLC Number：O17 Document ID：AReferences：[1]Ralston,A. ,A first Course in Numerical Analysis,Mc Graw-Hill,1965.[2]Saff,E. B. and Varga,R.S. ,On the Zeros and Poles of Padé Approximations to exp(x),Numer. Math. ,25(1975),1,1-4.[3]Wanner,G. ,Hairer,E. and Nqrsett,P. ,Order Stars and Stability Theorems,BIT,18(1978),4,475-489.[4]Yang Fengjian and Chen Xinming,A (a)-acceptability of Padé Approximations to Function exp (q). Approx. Thory & its Appl.,15 (1999)3,92- 99.[5]Liniger,W. and Willoughby,R. A.,Efficient Integration Methods for Stiff Systems of Ordinary Differential Equations,SIAM J. Numer. Anal. ,7(1970),1,47- 66.[6]Li Shoufu and Yang Fengjian,Acceptability of Rational Approximations to the Function exp (q) (in Chinese),Math,Numer Sinica,14 (1992),4,480- 488.[7]Yang Fengjian,The necessary and Sufficient Conditions of A-Acceptability of n parameters (n,n) Rational Approximations to the Function exp (q) (in Chinese). Math Numer Sinica,18(1996),4,397-404.[8]Zhong Y. Q.,Complex Analysis (in Chinese),Higher Education Press,Beijing,1979.[9]Nrsett,S. P. ,C-Polynomials for Rational Approximation to the Exponential Function,Numer. Math. ,25(1975),1,39-56.Manuscript Received：1999年9月14日Manuscript Revised：2000年12月2日Published：2001年9月1日