A subset T of the free monoid \(X^*\) on a finite alphabet X is said to be an infix code if u,xuy\(\in T\) \(\Rightarrow\) \(xy=1\). An infix congruence is a congruence on \(X^*\) whose classes are infix codes; if these classes are also finite, the congruence is said to be f- disjunctive. The author starts by developing elementary aspects of the general theory of infix congruences, obtaining, in particular, the following: (1) an example of an infix congruence which is not f- disjunctive; (2) every commutative infix congruence is f-disjunctive; (3) every infix cancellative congruence is the syntactic congruence of some language; (4) every commutative congruence, maximal subject to being infix, is cancellative; (5) an easily verifiable necessary and sufficient condition for two words to be distinguished by some commutative cancellative infix congruence. The main result characterizes the congruences in (4) as the kernels of homomorphisms from \(X^*\) into the additive monoid of natural numbers. The proof involves techniques of the theory of topological vector spaces.