Intrinsic state molecular pseudoconnectivity indices, i.e., indices which are based on the intrinsic state concept and which are built on the intrinsic and the electrotopological state values, are used to model different properties of different classes of molecules: the side-chain molecular volume, the isoelectric point, the melting temperatures, the solubility, the specific rotations, and the crystal density of amino acids, the motor octane number and the melting temperatures of alkanes, the lattice enthalpy of metal halides, and the singlet excitation energies of DNA/RNA bases. A series of three activities an also modeled: the rates of hydrogen abstraction, the minimum anesthetic concentrations of chlorofluoroalkanes, and the antagonism of adrenalin by 2-bromo-2-phenethylamines. The modeling of the properties has been compared with the modeling achieved by the well-known molecular connectivity indices, while the modeling of the activities is compared with the modeling achieved by specific E-state indices. A comparison with the modeling power of the molar masses is also always stressed. Molecular pseudoconnectivity terms derived by a trial-and-error procedure are the best descriptors for the melting temperatures and crystal density of amino acids, both properties of alkanes, the. lattice enthalpy of metal halides, the singlet excitation energies of DNA/RNA bases, the minimum anesthetic concentration, and the adrenalin antagonism. Further, a molecular pseudoconnectivity term of chlorofluoroalkanes, where subclasses of compounds share the same value of connectivity indices, is the best dominant descriptor for the rates of hydrogen abstraction. The advantage of these intrinsic state derived descriptors is rendered even more evident in the study of the activity of 2-bromo-2-phenethylamines, where many compounds show redundant connectivity and valence connectivity values. The modeling of the solubility of amino acids with pseudoconnectivity descriptors requires the introduction of supra-pseudoconnectivity descriptors, a fact that mimics a result already obtained with molecular connectivity indices. Sometimes a combination of molecular connectivity and pseudoconnectivity indices achieves a remarkable modeling.