If you are aiming for a stay abroad as a postdoc after gaining your doctorate, you may apply for a Postdoc.Mobility fellowship. The SNSF also offers smaller grants for researchers at postdoc level, namely Scientific Exchanges.
In addition, the SNSF finances postdoctoral posts as part of project funding and via career funding schemes (Eccellenza, PRIMA, partially Ambizione) and programmes (NCCRs, NRPs, special programmes for biology and medicine, Sinergia). The PhD posts are awarded to the researchers responsible for the project.
If you are a postdoc with family commitments working in an SNSF-funded project, you may be able to reduce your work-time percentage or have child care costs covered via a Flexibility Grant (the two forms of support may also be combined).
Flexibility Grant