  The modular case of the Andr\'e-Oort Conjecture is a theorem of Andre and
Pila, having at its heart the well-known modular function j. I give an overview
of two other `nonclassical' classes of modular function, namely the
quasimodular (QM) and almost holomorphic modular (AHM) functions. These are
perhaps less well-known than j, but have been studied by various authors
including for example Masser, Shimura and Zagier. It turns out to be sufficient
to focus on a particular QM function $\chi$ and its dual AHM function $\chi^*$,
since these generate the relevant fields. After discussing some of the
properties of these functions, I go on to prove some Ax-Lindemann results for
$\chi$ and $\chi^*$. I then combine these with a fairly standard method of
o-minimality and point counting to prove the central result of the paper; a
natural analogue of the modular Andr\'e-Oort conjecture for the function
$\chi^*$.
