The nonlinear microwave response of superconducting YBa2Cu3O7−&dgr;thin films and crystals was studied quantitatively by measuring the third-order harmonic amplitudeE3&ohgr;(&ohgr;: 35 GHz,jRF⩽3×104A/cm2). We findE3&ohgr;to be dominated by twoextrinsiceffects: (1) the interaction with flux lines in weak links, leading to an increased nonlinear response at low temperatures, and (2) rf related flux line creation at film edges, yielding a highE3&ohgr;-signal close toTc.Both effects together lead to a minimum inE3&ohgr;around 40–60 K, which makes this temperature interval interesting for rf applications. Intrinsic nonlinearities are smaller by orders of magnitude and could not be detected. ©1997 American Institute of Physics.