Let \(f\) be a continuous function on a two-dimensional surface \(M\) with a discrete set \(E\) of local extrema such that for any point outside of \(E\) there exists a suitable neighborhood \(U\) so that \(f|_U\) is topologically conjugate to the function \(\operatorname{Re} z^n\) in a neighborhood of zero for some \(n\in \mathbb N\). If \(M\) is a compact surface then the quotient space of \(M\) with respect to its partition formed by the components of the level sets of \(f\) is a topological graph; it is called the Kronrod-Reeb graph of \(f\) (cf. [A. S. Kronrod, Usp. Mat. Nauk 5, No. 1(35), 24–134 (1950; Zbl 0040.31603); G. Reeb, C. R. Acad. Sci., Paris 222, 847–849 (1946; Zbl 0063.06453)]). The author studies the case of noncompact surfaces. In particular, he describes sufficient conditions under which the corresponding quotient is a graph with stalks.