In this article we analyse parametric linear fractional programming problems. In these problems all coefficients of the numerator and (or) of the denominator of the objective function and (or) all right hand sides are parameters. The analysis deals with the characterization of the set of those parameters, for which the supremum of the objective function of such a problem is finite resp. the problem is solvable. In further deals with the form and the qualities of local stability sets, of a unique partition of the solvability set and qualities of the supremum-function and the solution-function. All researches we made without any algorithm for linear fractional programming problems.