The nature of the (CHF)-F-... H-bond is studied by examining the potential energy surfaces for dimers of the fluoromethanes, including all homo- and heterodimers involving CH4, CFH3, CF2H2, CF3H, and CF4. Several of the surfaces encompass two separate minima. Any pair capable of forming a cyclic structure does so, this geometry being more stable than any other minima that might occur on the surface. Such cyclic dimers are bound by 2-3 kcal/mol. Noncyclic geometries are only very weakly bound. In all cases, the C-H bonds that participate directly in the H-bonds undergo a contraction and associated blue shift in their stretching frequencies, whereas the C-F bonds manifest an elongation. The most strongly bound of all dimers studied pairs CH3F with CHF3, for which the C-H bond contracts by 0.0023 Angstrom, and its stretching frequency increases by 39 cm(-1). The most stable cyclic dimer of fluoroform, containing one single and one bifurcated hydrogen bond, is reported for the first time and thus resolves the longstanding problem of the structure of the fluoroform dimer.