Localized orbital methodsare used in this paper for estimating several electronic properties of carbon nanotubes as well as of Be and Mg oxides, sulphides and selenides, in both zincblende and rocksalt structures. Calculations have been performed with the Discrete-Variational-Method (DVM), a real space first-principles local-density-functional approach. Comparison with the experiment and with other first-principles approaches show that the electronic and structural properties of solids can be computed with DVM at least as accurately as with other methods. Advantages of the myethod for what attains to the required computational effort, especially when a large number atoms has to be included in the system, will be presented, as well as some discussion on the physical relevance of the results we obtained.