The notion of mixed quermassintegrals in the classical Brunn-Minkowski theory is extended to that
of Orlicz mixed quermassintegrals in the Orlicz Brunn-Minkowski theory. The analogs of the classical Cauchy-
Kubota formula, the Minkowski isoperimetric inequality and the Brunn-Minkowski inequality are established
for this new Orlicz mixed quermassintegrals.