Astrophysics research has typically an international dimension, since most of the projects require large collaborations. Many scientific projects are conducted by international teams. It is therefore essential that young researchers have the opportunity to work with teams in different countries.INAF – the Italian Institute for Astrophysics- intends to launch a programme of incoming mobility for researchers non-resident in Italy. The AstroFIt programme here proposed will allow INAF to set up for the first time such a programme.The fellowships will be carried out at INAF structures, that include 19 Institutes broadly distributed in Italy and the Telescopio Nazionale Galileo (TNG) in the Canary Island.Two mobility types will be implemented: a) Incoming Mobility and b) Re-integration fellowships. Both types are of utmost importance for INAF, considering the so-called “brain drain” phenomenon, not counterbalanced by an adequate attractiveness of Italian research centres for foreign scientists. Both the proposed types of fellowship try to invert this tendency.The limited number of fellowships foreseen is due to the fact that AstroFIt Programme is an integration of other international scientific collaborations, schemes and initiatives in which INAF is already involved. Nevertheless, Astrofit is important because unrelated to a single scientific programme but is devised to the strenghthening of the fellows capabilities in working in an environment different from the environment where initial training was achieved.The program will be 4-year long. Fourteen (14) fellowships will be offered, with two calls, each one including 3 Incoming mobility fellowships and 4 Re-integration fellowships. Every fellowship will last two years. All the fellowships will be easily completed within its 4-year duration, including a final meeting to present and discuss the programme results..