  Let $F$ be a function field over $\mathbb{F}_q$, $A$ its ring of regular
functions outside a place $\infty$ and $\mathfrak{p}$ a prime ideal of $A$.
First, we develop Hida theory for Drinfeld modular forms of rank $r$ which are
of slope zero for a suitably defined Hecke operator
$\mathrm{U}_{\mathfrak{p}}$. Second, we show the existence in the finite slope
case of families of Drinfeld modular forms varying continuously with respect to
the weight. Finally, we show a classicity result: an overconvergent Drinfeld
modular form of sufficiently small slope with respect to the weight is a
classical Drinfeld modular form.
