Linear integral equations of the third kind are studied as equations in two different spaces of generalized functions. In the first space $D_\tau $, which consists of linear combinations of delta functions and continuous functions, the equation of the third kind has properties similar to those of the Fredholm equation of the second kind. The second space $P_\tau $ is comprised of linear combinations of delta functions and functions continuous except for poles, integration over the poles being defined by Cauchy’s principal value. $\ln P_\tau $ the behavior of the third-kind equation is essentially different from that of second-kind Fredholm equations. Solutions in both $D_\tau $ and $P_\tau $ may be constructed explicitly via Fredholm theory. Examples showing the suitability of these spaces in physical problems are cited, and earlier literature on third-kind equations is surveyed briefly.