Off-resonant electric field induced second harmonic generation (EFISH) and resonant third harmonic generation (THG) measurements of two squarylium dyes are reported. The magnitude of gamma is large for both processes. The EFISH measurement clearly shows that the off-resonant third-order polarizability is negative, a consequence of the dominance of a non-two-photon mechanism. This unusual result is in agreement with our earlier reports on two other squarylium dyes. Resonant THG measurements strongly suggest that the two-photon contribution, while smaller than the one-photon contribution, is not negligible and cannot be entirely ignored when defining the overall third-order optical susceptibility. Consequently, the squaryliums are best qualitatively described by a three-level model that truncates to two dominant perturbation terms. Also reported is the isomeric distribution of squaryliums. Proton NMR results are interpreted by way of molecular mechanics to show that the squaryliums can readily exist as a mixture of isomers. The possible effects on nonlinear optical (NLO) measurements via an orientational contribution to the EFISH gamma are discussed. An X-ray structure for the squarylium dye TSQ is presented and interpreted. The X-ray structure clearly suggests that the squarylium dyes are extensively bond delocalized with relatively little bond length alternation.