The constraints on combinations of nearest neighbors in nucleic acid sequences and the numbers of independent sequences needed to describe nearest-neighbor properties of oligomers and polymers are derived and summarized. It has been pointed out in previous work [D. M. Gray and I. Tinoco, Jr. (1970) Biopolymers, Vol. 9, pp. 223-244; R. F. Goldstein and A. S. Benight (1992) Biopolymers, Vol. 32, pp. 1679-1693] that these constraints restrict the information available from measurements of properties of sequence combinations. The emphasis in this paper is on the properties of oligomer sequences that vary in length, where each nucleotide or base pair at the end of the sequence makes a significant contribution to the measured property by interacting with its boundary of fixed sequence or solvent. In such cases it is not be possible to determine values of properties of individual nearest neighbors, except for the like neighbors [e.g., d(A-A), d(G-G), d(T-T), and d(C-C) nucleotide neighbors in single-stranded DNA or d(A-A)/d(T-T) and d(G-G)/d(C-C) base pair neighbors in double-stranded DNA], solely from measurements of properties of different sequences. Even values for properties of the like neighbors cannot be determined from such oligomeric sequences if the sequences are all of the same length. Nearest-neighbor properties of oligomer sequences that vary in length can be summarized in terms of the values for independent sets of sequences that are nearest neighbors and monomers all with boundaries of the fixed sequence or solvent. Straightforward combinations of the values for the independent sequences will give the values of the property for any dependent sequence, without explicit knowledge of the individual nearest-neighbor values. These considerations have important consequences for the derivation of widely used thermodynamic parameters, as discussed in the following paper.