The final step in the mathematical treatment of many problems in such fields as radiative transfer, neutron transport, and optimal filtering theory involves the solution of a Fredholm integral equation in which the kernel is degenerate or can be closely approximated by a degenerate kernel. The standard procedure for solving such an equation is to convert it into an equivalent matrix equation and compute the solution by evaluating a number of integrals and performing a matrix inversion. This last step, however, can present serious computational difficulties. In this study, invariant imbedding techniques are used to convert the Fredholm equation into an initial-value problem, and the troublesome matrix inversion is replaced in this formulation by solving a Riccati system of differential equations. 8 pp. Refs.