Convective models have been constructed for stars of mass M<0.1M0.. For a given mass, the internal structure of the star is computed at several radii, taking into account nonrelativistic degeneracy of the stellar material. It is found that for these stars the central temperature has a maximum value at one particular radius and this value decreases when the radius is greater or smaller. For example, for a Population I star of mass 0.05Mo. the maximum temperature of two million degrees occurs at a radius of 0.12R0., and the temperature decreases if we increase or decrease the radius. For Population I stars with mass less than 0.05 M0. the central temperatures and densities are too low for energy production by the proton-proton cycle and even for a star of mass 0.07Mo. this process may not produce sufficient energy. Application of these models is made to contracting stars and it is found that Population I stars of mass less than 0.05M0. become degenerate objects and that they do not reach the main-sequence stage. The limiting mass for such an evolution may be as high as 0.07M . For a star of mass 0.05Mo., the time scale for contraction to the stage of maximum central temperature is estimated to be approximately one billion years, which is small as compared with the age of the galaxy. After this stage the star begins to cool slowly and evolves towards a completely degenerate configuration. Thus it becomes a "black" dwarf without ever going through normal stellar evolution.