  We study the formation of classical singularities in Generalized Brans-Dicke
theories that are natural extensions to Brans-Dicke where the kinetic term is
modified by a new coupling function $\omega(\varphi)$. We discuss the
asymptotic limit $\omega(\varphi)\rightarrow\infty$ and show that the system
generically does not approach General Relativity. Given the arbitrariness of
$\omega(\varphi)$, one can search for coupling functions chosen specifically to
avoid classical singularities. However, we prove that this is not the case.
Homogeneous and spherically symmetric collapsing objects form singularities for
arbitrary coupling functions. On the other hand, expanding cosmological
scenarios are completely free of Big Rip type singularities. In an expanding
universe, the scalar field behaves at most as stiff matter, which makes these
cosmological solutions asymptotically approach General Relativity.
