We obtained 0.8È2.4 km spectra at a resolution of 320 km s~1 of four narrow-line Seyfert 1 galaxies in order to study the near-infrared properties of these objects. We focus on the analysis of the Fe II emission in that region and the kinematics of the low-ionization broad lines. We show that the 1 km Fe II lines (j9997, j10501, j10863, and j11126) are the strongest Fe II lines in the observed interval. For the Ðrst time, primary cascade lines of Fe II arising from the decay of upper levels pumped by Lya Ñuores-cence are resolved and identiÐed in active galactic nuclei. Excitation mechanisms leading to the emission of the 1 km Fe II features are discussed. A combination of Lya Ñuorescence and collisional excitation is found to be the main contributor. The Ñux ratio between near-IR Fe II lines varies from object to object, in contrast to what is observed in the optical region. A good correlation between the 1 km and optical Fe II emission is found. This suggests that the upper z4F0 and z4D0 levels from which the bulk of the optical Fe II lines descend are mainly populated by the transitions leading to the 1 km lines. The width and proÐle shape of Fe II j11127, Ca II j8642, and O I j8446 are very similar but signiÐcantly narrower than Pab, giving strong observational support to the hypothesis that the regions where Fe II, Ca II, and O I are produced are cospatial, interrelated kinematically, and most probably located in the outermost portion of the broad-line region.