  Very-high-energy gamma-ray flares of TeV blazars are generally accompanied by
simultaneous flaring activity in X-rays. The recent observations by the Whipple
collaboration of an ``orphan'' TeV flare of 1ES 1959+650 (without simultaneous
X-ray flare) is very hard to reconcile with the standard leptonic SSC model
which is routinely very successfully employed to explain the SED and spectral
variability of TeV blazars. In this paper, an alternative scenario is suggested
in which the ``orphan'' TeV flare may originate from relativistic protons,
interacting with an external photon field supplied by electron-synchrotron
radiation reflected off a dilute reflector. While the external photons will be
virtually ``invisible'' to the co-moving ultrarelativistic electrons in the jet
due to Klein-Nishina effects, their Doppler boosted energy is high enough to
excite the $\Delta$ resonance from relativistic protons with Lorentz factors of
~ 10^3 - 10^4. This model is capable of explaining the ``orphan'' TeV flare of
1ES 1959+650 with plausible parameters, thus constraining the number and
characteristic energy of relativistic protons in the jet of this blazar.
