Three periods can be distinguished in university patenting at the U.S. Patent and Trade Office (USPTO) since the Bayh-Dole Act of 1980: (1) a first period of exponential increase in university patenting till 1995 (filing date) or 1999 (issuing date); (2) a period of relative decline since 1999; and (3) in most recent years -- since 2008 -- a linear increase in university patenting. We argue that this last period is driven by specific non-US universities (e.g., Tokyo University and Chinese universities) patenting increasingly in the U.S.A. as the most competitive market for high-tech patents.