We compute the complete leading-log terms of the next-to-next-to-next-to-le
ading-order corrections to potential NRQCD. As a by-product we obtain the l
eading logs at O(m alpha(s)(5)) in the heavy quarkonium spectrum. These lea
ding logs, when Lambda(QCD) <<m alpha(s)(2), give the complete O(m alpha(s)
(5)ln alpha(s)) corrections to the heavy quarkonium spectrum. (C) 1999 Publ
ished by Elsevier Science B.V. All rights reserved.