  We explore aspects of the phase structure of SU(2) and SU(3) lattice gauge
theories at strong coupling with many flavours $N_f$ of Wilson fermions in the
fundamental representation. The pseudoscalar meson mass as a function of
hopping parameter is observed to deviate from the expected analytic dependence,
at least for sufficiently large $N_f$. Implications of this effect are
discussed, including the relevance to recent searches for an infrared fixed
point.
