Many random alloys of heavy fermion systems exhibit the so-called non-
Fermi-liquid behavior. An example of such a system is U1-xThxPd2Al3 in
which the uranium (U) sites are randomly replaced by thorium (Th). In
the doping range 0.4 < x < 0.8 the temperature dependence of specific
heat coefficient, susceptibility and resistivity are all at odds with
the well-documented fermi liquid behavior of pure heavy fermion mater
ials such as CeAl3 or UPt3. In this paper we extend the electronic pol
aron theory for heavy fermion systems to include the elastic scatterin
g of the broad band electrons due to randomness and show that the unus
ual behavior of the alloys are well accounted for without further assu
mptions. We will also show that doping has profound effects on the mag
netic ordering properties, and many of our predictions have been obser
ved.