  A canonical analysis of RG improved action of the Einstein-Hilbert functional
is performed. The gravitational and cosmological constants as function of the
space-time coordinates are treated as external non-geometrical fields. Dirac's
constraint analysis is performed, in the general case, up to secondary
constraints. The constraints are second class and, in general, the problem
appears to be technically complicated. This fact suggests studying the Dirac's
constraint analysis of the related Brans-Dicke theory. It exhibits a Dirac's
constraint algebra similar to Einstein's geometrodynamics except that the
Poisson Brackets between Hamiltonian-Hamiltonian constraints is not only linear
combination of the momentum constraints but also of a term note reducible to
linear combination of the constraint and proportional to the extrinsic
curvature. This shows that Branse-Dicke geometrodynamics is inequivalent to
Einstein General Relativity geometrodynamics.
