  We demonstrate that a model of disordered Anderson lattices can account for
many non-Fermi liquid features observed in a number of Kondo alloys. Due to the
exponential nature of the Kondo temperature scale, even moderate disorder leads
to a rather broad distribution of Kondo temperatures, inducing strong effective
disorder seen by the conduction electrons. Spins with very small Kondo
temperatures remain unquenched and dominate the low temperature properties. The
model predicts logarithmic divergences in thermodynamic quantities at low
temperatures. We also find a linear temperature dependence of the resistivity,
a feature that remained a stumbling block in previous theoretical attempts. We
argue that for realistic amounts of disorder, such marginal Fermi liquid
behavior is a very robust feature of disordered Kondo alloys.
