loss due to different alternative processes.

A reliable quantitative theory of the mass loss rate in the Population III stars is still missing, but it is of great interest to investigate the possible consequences of the mass loss on the properties of these stars. For this purpose we extend hereby our calculations of the conservative case of the first-stars evolution in PaperI assuming a mass loss rate given by an ad-hoc parametrization.

This work is organized as follows: In Sect.\[massloss\] the mass loss mechanisms are reviewed. In Sect.\[results\] we describe the initial conditions and results of the computed models, the main physical variables and their properties. Then, in Sect.\[discussion\] we discuss our results in comparison with the conservative case. Finally, in Sect.\[conclusions\] we summarize the conclusions.

Mass Loss Mechanisms \[massloss\]
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The mass loss in stars of Population I and II has been studied both theoretically and observationally. However, an extrapolation of the results to stars of Population III is questionable due to very different physical properties of both the interiors as well as the atmospheres of the stars.

Regarding the short lifetimes of the massive first stars, their mass loss rates have thus to be estimated from the theoretical 