In this paper we describe the application in QSPR/QSAR studies of a new group of molecular descriptors: atom, atom-type and total linear indices of the molecular pseudograph's atom adjacency matrix. These novel molecular descriptors were used for the prediction of boiling point and partition coefficient (log P), specific rate constant (log k), and antibacterial activity of 28 alkyl-alcohols and 34 derivatives of 2-furylethylenes,respectively. For this purpose two quantitative models were obtained to describe the alkyl-alcohols' boiling points. The first one includes only two total linear indices and showed a good behavior from a statistical point of view (R(2) = 0.984, s = 3.78, F = 748.57,q(2) = 0.981, and s(cv) = 3.91). The second one includes four variables [3 global and 1 local(heteroatom) linear indices] and it showed an improvement in the description of physical property (R(2) = 0.9934, s = 2.48, F = 871.96, q(2) = 0.990, and s(cv) = 2.79). Later, linear multiple regression analysis was also used to describe log P and log k of the 2-furyl-ethylenes derivatives. These models were statistically significant [(R(2) = 0.984, s = 0.143, and F = 113.38) and (R(2) = 0.973, s = 0.26 and F = 161.22), respectively] and showed very good stability to data variation in leave-one-out (LOO) cross-validation experiment [(q(2) = 0.93.8 and scv = 0.178) and (q(2) = 0.948 and s(cv) = 0.33), respectively]. Finally, a linear discriminant model for classifying antibacterial activity of these compounds was also achieved with the use of the atom and atom-type linear indices. The global percent of good classification in training and external test set obtained was of 94.12% and 100.0%, respectively. The comparison with other approaches (connectivity indices, total and local spectral moments, quantum chemical descriptors, topographic indices and E- state/biomolecular encounter parameters) reveals a good behavior of our method. The approach described in this paper appears to be a very promising structural invariant, useful for QSPR/QSAR studies and computer-aided "rational" drug design.