This paper deals with the Gomory all-integer algorithm and its modification to obtain integer solutions to linear fractional functionals programming (L.F.F.P.). First, we sholve a non integer L.F.F.P.-problem, then we define linear substitutional objective functions and derive important properties of them. we find the integer solution to the L.F.F.P.-problem by solving linear programming problems with these substitutinal objective functions. All cases, in which the integer L.F.F.P.-problem has a solution, are described and th4 algorithms, to find the optimal integer solution, are given. We can see, that there are more cases, in which the integer L.F.F.P.-problem has a solution than in finding a solution of the L.F.F.P.-problem due to Martos.