The noncommutative analytic Toeplitz algebra \(F_n^\infty\) is the weakly closed algebra generated by the left creation operators on the full Fock space \(F^2(H_n)\) on \(n\) generators, and the identity. Let \(\mathcal X\) be a complex linear space and let \(L({\mathcal X})\) be the space of all linear operators on \(\mathcal X\). For two Hilbert spaces \({\mathcal L},{\mathcal H}\), let \(B({\mathcal L},{\mathcal H})\) be space of all bounded linear operators from \(\mathcal L\) into \(\mathcal H\). The author studies the following Nudel'man type interpolation problem in several variables: Given a nonnegative integer \(k\), some operators \(A_1,\ldots,A_n\) in \(L({\mathcal X})\), and \(x,y\in\mathcal X\), find conditions for the existence of an element \(f\in F_n^\infty\bar\otimes B(\mathcal L,H)\) with \(\|f\|_\infty \leq 1\), and an inner element \(\psi\in F_n^\infty\bar\otimes B(\mathcal L,H)\) with dim \(\psi[F^2(H_n)\otimes{\mathcal L}]^\perp\leq k\) such that \(f(A_1,\ldots,A_n)x=\psi(A_1,\ldots,A_n)y\) or \(f(A_1,\ldots,A_n)^*x=\psi(A_1,\ldots,A_n)^*y\). The main result of the paper is, in fact, an indefinite generalization of the definite Nudel'man type theorems (obtained by Nudel'man himself as well as by M. Rosenblum and J. Rovnyak). Among several consequences, the author obtains a new Carathéodory-Fejér and Nevanlinna-Pick type interpolation theorem for meromorphic operators on Fock spaces. The author mentions that some results of a preprint by J. Rovnyak (in the case \(n=1\)) overlap a part of his assertions in the work under review, a fact of which he became aware after submitting the paper for publication.