Ab initio calculations with the 6-31G** basis set are used to examine the structure and energetics of H3X-HF-HF (X = N, P). Only one minimum is located on the potential energy surface in each case. The fully optimized geometries are quite bent, with ��(XFF) equal to about 70°, and may be described as cyclic, containing two strong H bonds and one much weaker interaction between the terminal subunits. Each trimer is held together by an interaction energy considerably higher than the sum of H-bond energies of the two constituent dimers; three-body terms are -4.1 and -1.4 kcal/mol for the N and P cases, respectively. The geometries provide additional evidence of cooperativity: addition of the third subunit to a preexisting dimer leads to contraction of the H-bond length and further stretching of the HF bonds. The latter elongations are directly proportional to reductions in the calculated stretching force constants, experimental vibrational frequency shifts, and integrated band intensities.