  Let $I$ be an inner function in the unit disk $\mathbb D$ and let $\mathcal
N$ denote the Nevanlinna class. We prove that under natural assumptions, Bezout
equations in the quotient algebra $\mathcal N/I\mathcal N$ can be solved if and
only if the zeros of $I$ form a finite union of Nevanlinna interpolating
sequences. This is in contrast with the situation in the algebra of bounded
analytic functions, where being a finite union of interpolating sequences is a
sufficient but not necessary condition. An analogous result in the Smirnov
class is proved as well as several equivalent descriptions of Blaschke products
whose zeros form a finite union of interpolating sequences in the Nevanlinna
class.
