Variable-temperature H-1 and C-13 NMR spectra have been obtained for solutions of lanthanide(III) complexes derived from 1,4,7,10-tetrakis(N,N-diethylacetamido)-1,4,7,10-tetraazacyclododecane in deuterated acetonitrile. The lanthanide-induced shifts (LIS) observed in the spectra of the paramagnetic complexes (Ln = Pr, Nd, Sm, Eu, Tb, Dy, Ho, Er, Tm, and Yb) are analyzed using a linear least-squares procedure involving the five componenents of the traceless part of the magnetic susceptibility tenser as fitting parameters (C-13 data is limited to Ln = Pr, Nd, Sm, and Eu). No assumptions are made regarding the orientation of the molecular coordinate system and principal magnetic axis system in this method of analysis. Furthermore, by using a linear least-squares fitting of the data, we establish that it is possible to allow a computer program to permute LIS values over any number of nuclei and determine which particular assignment gives the best fit of the LIS data. A new method of evaluating the contact component of the LIS in the proton spectra is introduced. Molecular mechanics calculations are combined with analyses of LIS data to determine structures of the complexes in solution. Through such an approach, we establish that the eight-coordinate lanthanide ions are encapsulated by the octadentate macrocyclic ligand, with the four nitrogen atoms and four oxygen atoms situated at the vertices of a distorted square antiprism having C-4 symmetry (the rotational angle between the two square pyramids is 47 degrees). The lanthanide ions lie above the plane of nitrogen atoms of the macrocycle, with the distance decreasing from 1.74 to 1.41 Angstrom across the lanthanide series. The distance to the mean plane of donor oxygen atoms increases from 0.63 to 0.83 Angstrom across the series. The Ln(3+)-N and Ln(3+)-O bond distances range from 2.82 to 2.54 Angstrom and 2.47 to 2.21 Angstrom, respectively. The NMR data establish that each complex exists in solution as a single pair of enantiomers. Analysis of the LIS data establishes that the isomer with each ethylenediamine ring of the macrocycle in the lambda conformation with clockwise rotation of the pendant arms, or its enantiomer, is favored in solution.