  Consider a scaled Nevanlinna-Pick interpolation problem and let $\Pi$ be the
Blaschke product whose zeros are the nodes of the problem. It is proved that if
$\Pi$ belongs to a certain class of inner functions, then the extremal
solutions of the problem or most of them, are in the same class. Three
different classical classes are considered: inner functions whose derivative is
in a certain Hardy space, exponential Blaschke products and also the well known
class of $\alpha$-Blaschke products, for $0<\alpha<1$.
