  In the present work some generalizations of the Hawking singularity theorems
in the context of $f(R)$ theories are presented. The assumptions are of these
generalized theorems is that the matter fields satisfy the conditions
$\bigg(T_{ij}-\frac{g_{ij}}{2} T\bigg)k^i k^j\geq 0$ for any generic unit time
like field, that the scalaron takes bounded positive values during its
evolution, and that the resulting space time is globally hyperbolic. Then, if
there exist a Cauchy hyper surface $\Sigma$ for which the expansion parameter
$\theta$ of the geodesic congruence emanating orthogonally from $\Sigma$
satisfies some specific conditions, it may be shown that the resulting space
time is geodesically incomplete. Some mathematical results of reference
\cite{fewster} are very important for proving this. The generalized theorems
presented here apply directly some specific models such as the Hu-Sawicki or
Starobinsky ones \cite{especif3}, \cite{capoziello4}. However, for other
scenarios, some extra assumptions should be implemented for the geodesic
incompleteness to take place. However, the negation of the hypothesis of these
results does not necessarily imply that a singularity is absent, but that other
mathematical results should be considered to prove that.
