In the present paper the author develops a conception for solving combinatorial programming problems.There is used an extension principle resting upon the following basic idea: LetSbe the set of admissible solutions for the initial problem. Then one defines such a setRthatR∩Scontains a t least one optimal solution of the given problem. Using the elements of a sequence {bν} of real numbers one considers step by step subsetsUν ofRand for their elements it is inspected if they belong toSor not. The requirementsRandUν have to satisfy secure the existence of a setUϱ containing an optimal solution of the given problem. Such a solution surely will be known after finitely many steps by means of the optimality criterion formulated in the paper. Having founded in general the extension principle the author gives a procedure for solving the linear assignment problem and an algorithm for the travelling salesman problem both basing on the extension principle.