In observations made with the Whipple 10 m telescope, 1ES 1959+650 (z = 0.048) was caught in a high flaring state in May 2002, concurrent with a high X-ray state, and in June 2002, for which there was no corresponding X-ray flare. The spectra for both of those occasions are well fitted by a power law of differential spectral index ∼ -2.8. The relative stability of the spectral index for those flares argues strongly in favour of a two-component model as to the emission zones for the two radiation regimes. Markarian 421 (z = 0.031) was observed to be in a high flaring state, at levels of ≥ 3 Crab, during March and April 2004. The average spectrum over this time period shows evidence for a cut-off in the spectrum at ∼ 5 TeV, similar to a cut-off seen during an equivalently strong episode of flaring activity in 2001. The continued appearance of this feature indicates a long term stability, either in the physical conditions at the source, or in the intervening medium (such as attenuation on the extra-galactic infra-red background radiation).