Given vectors $x$ and $y$ in a Hilbert space, an interpolating operator is a bounded operator $T$ such that $Tx=y$. An interpolating operator for ${\bold N}$ vectors satisfies the equation $Tx_i =y_i$, for $i=1,2,\cdots,n$. In this article, we investigate self-adjoint interpolation problems in CSL-Algebra Alg$\Cal L$.