We describe nucleic acid triple-helical structures containing either amide or 2'-5' linkages, the former backbone describing the chemistry of certain peptide nucleic acids (PNA). The methodology and the starting reference frame are the same as those described in the preceding article. Apart from evaluating the possible combinations of chain conformations that connect adjacent bases on each of the three strands, we have examined the feasibility of tripler formation when neighboring Watson-Crick+Hoogsteen hydrogen-bonded base tripler are displaced by small amounts along their short and long axes. The predicted triple-helical complexes are examined in terms of relevant crystallographic, spectroscopic, and calorimetric data, The computed models clarify why PNA cannot form B-like structures and also reveal principles useful for the design of other triplex-forming DNA mimics.