  The ground state structures of the A$_x$B$_{1-x}$C wurtzite (WZ) alloys with
$x=$0.25, 0.5, and 0.75 are revealed by a ground state search using the
valence-force field model and density-functional theory total energy
calculations. It is shown that the ground state WZ alloy always has a lower
strain energy and formation enthalpy than the corresponding zinc-blende (ZB)
alloy. Therefore, we propose that the WZ phase can be stabilized through
alloying. This novel idea is supported by the fact that the WZ
AlP$_{0.5}$Sb$_{0.5}$, AlP$_{0.75}$Sb$_{0.25}$, ZnS$_{0.5}$Te$_{0.5}$, and
ZnS$_{0.75}$Te$_{0.25}$ alloys in the lowest energy structures are more stable
than the corresponding ZB alloys. To our best knowledge, this is the first
example where the alloy adopts a structure distinct from both parent phases.
