  The stability properties of the Einstein Static solution of General
Relativity are altered when corrective terms arising from modification of the
underlying gravitational theory appear in the cosmological equations. In this
paper the existence and stability of static solutions are considered in the
framework of two recently proposed quantum gravity models. The previously known
analysis of the Einstein Static solutions in the semiclassical regime of Loop
Quantum Cosmology with modifications to the gravitational sector is extended to
open cosmological models where a static neutrally stable solution is found. A
similar analysis is also performed in the framework of Horava-Lifshitz gravity
under detailed balance and projectability conditions. In the case of open
cosmological models the two solutions found can be either unstable or neutrally
stable according with the admitted values of the parameters.
