  The theory of linear Fredholm integral-functional equations of the second
kind with linear functionals and with a parameter is considered. The necessary
and sufficient conditions are obtained for the coefficients of the equation and
those parameter values, in the nighbohood of which the equation has solutions.
The leading terms of the asymptotics of the solutions are constructed. The
constructive method is proposed for constructing a solution both in the regular
case and in the irregular one. In the regular case, the solution is constructed
as a Taylor series in powers of the parameter. In the irregular case, the
solution is constructed as a Laurent series in powers of the parameter.
Constructive theory and method is demonstrated on the model example.
