Novel molecular descriptors based on local spectral moments of the bond matrix are defined. Mathematical expressions relating bond moments to linear combinations of structural fragments are derived. The novel descriptors are used to describe boiling points of alcohols producing a good QSPR model accounting for more than 98% of variance. A quantitative structure-reactivity model is obtained to predict the specific rate constant (log k) of the nucleophilic addition of mercaptoacetic acid to 2-furylethylene derivatives. The model accounts for more than 96% of the variance in log k. Two other models were also obtained by using molecular connectivity indices and total spectral moments of the bond matrix that account for <84% of the variance in this reactivity index. A model based on quantum chemical descriptors accounts for the same variance than that obtained with bond moments. The model based on local moments permitted to compute the contribution of different structural fragments to the reactivity, and a good relationship (r = 0.98) was obtained with these group contributions with Hammett sigma(p) constants for 21 groups.