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Consider a scaled Nevanlinna-Pick interpolation problem and let $\Pi$ be theBlaschke 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 extremalsolutions of the problem or most of them, are in the same class. Threedifferent classical classes are considered: inner functions whose derivative isin a certain Hardy space, exponential Blaschke products and also the well knownclass of $\alpha$-Blaschke products, for $0<\alpha<1$.

Extremal solutions of Nevalinna-Pick problems and certain classes of inner functions