The iterated translative versions of classical kinematic integral formulae
for intrinsic volumes and curvature measures have led to a series of mixed
functionals and mixed measures of convex bodies. Here, we present a systema
tic study of the integral geometric relations which hold for these mixed me
asures and functionals. We give new formulae involving halfspaces, reductio
n formulae and some spherical representations and also generalize some earl
ier results.