For $p>1$ the Privalov space $N^p$ consists of all holomorphic functions $f$ on the open unit disk $\Bbb D$ for which $$ \sup_{0\leq r<1}\int_0^{2\pi}(log^+|f(re^{i\theta})|^p\frac{d\theta}{2\pi} <\infty. $$ We study the interpolation problems for the spaces $N^p$. Our results and methods are similar to those obtained by N. Yanagihara in [24] for the Smirnov class $N^+$.