  We investigate the evolution of low-mass metal-free Population III stars.
Emphasis is laid upon the question of internal and external sources for
CNO-elements, which - if present in sufficient amounts in the hydrogen-burning
regions - lead to a strong modification of the stars' evolutionary behavior.
For the production of carbon due to nuclear processes inside the stars, we use
an extended nuclear network, demonstrating that hot pp-chains do not suffice to
produce enough carbon or are less effective than the triple3-alpha-process. As
an external source of CNO-elements we test the efficiency of pollution by a
nearby massive star combined with particle diffusion. For all cases
investigated, the additional metals fail to reach nuclear burning regions
before deep convection on the Red Giant Branch obliterates the previous
evolution. The surface abundance history of the polluted Pop III stars is
presented. The possibilities to discriminate between a Pop II and a polluted
Pop III field star are also discussed.
