  In the first order formalism of gravitational theories, the spacetime
connection is considered as an independent variable to vary together with the
metric. However, the metric still generates its Levi-Civita connection that
turns out to determine the geodesics of matter. Recently, "hybrid" gravity
theories have been introduced by constructing actions involving both the
independent Palatini connection and the metric Levi-Civita connection. In this
study a method is developed to analyse the field content of such theories, in
particular to determine whether the propagating degrees of freedom are ghosts
or tachyons. New types of second, fourth and sixth order derivative gravity
theories are investigated and the so called f(X) theories are singled out as a
viable class of "hybrid" extensions of General Relativity.
