Intramolecular N-H center dot center dot center dot O hydrogen bonds in 3-(aminomethylene)pyran-2,4-dione and its simple derivatives (F, Li, and BeH substituents) were analyzed theoretically. The systems were optimized at the B3LYP/6-311++ G(d, p) level of approximation. For some fluorine derivatives the corresponding tautomers with O-H center dot center dot center dot N intramolecular H-bonds were investigated, and for such pairs of tautomers, the calculations on transition states of the N- H center dot center dot center dot O double left right arrow N center dot center dot center dot H-O proton-transfer reaction were carried out. The geometrical and energetic parameters for these species were characterized. The topological parameters derived from Bader theory were also analyzed; these are characteristics of H-bond critical points and also of ring critical points. Besides N-H center dot center dot center dot O and O-H center dot center dot center dot N intramolecular hydrogen bonds, there are the other intramolecular interactions, mostly ionic such as Be+delta center dot center dot center dot(-delta), Li+delta center dot center dot center dot-delta O, and Li+delta center dot center dot center dot-delta F. The F center dot center dot center dot O interactions also exist for some of species investigated. They may be classified as energetically stabilizing ones since the corresponding bond paths and critical points exist. The numerous correlations and dependencies between geometrical, topological, and energetic parameters were detected and described.