  In this paper we make a detailed analysis of conservation principles in the
context of a family of fourth-order gravitational theories generated via a
quadratic Lagrangian. In particular, we focus on the associated notion of
energy and start a program related to its study. We also exhibit examples of
solutions which provide intuitions about this notion of energy which allows us
to interpret it, and introduce several study cases where its analysis seems
tractable. Finally, positive energy theorems are presented in restricted
situations.
