For PhD students under contract with SNF: mobility grants in projects.
For postdocs with or without an SNF contract: Postdoc.Mobility.
SNF offers a wide range of fundings to researchers: more info on SNF.
The bilateral programs of SERI (State Secretariat for Education, Research and Innovation) offer several kinds of funding to researchers living in Switzerland and aim to promote scientific cooperation and exchanges. These programs include mobility grants for young researchers living in Switzerland.
SERI has appointed six Swiss research institutions as "leading houses" to manage these bilateral programs:
Leading House for the Latin American Region: University of St. Gallen (view calls)
Leading House Asia: ETH Zurich (view calls)
Leading House for MENA (North Africa and Middle-East): HES·SO (more info)
Leading House for Africa: Swiss Tropical and Public Health Institute (Swiss TPH) in collaboration with University of Basel (more info)
Leading House for Russia and CIS region (*) : University of Geneva (view calls)
(*) Armenia, Azerbaijan, Belarus, Georgia, Kazakhstan, Kyrgyzstan, Moldova, Mongolia, Tajikistan, Turkmenistan, Ukraine and Uzbekistan
Leading House for Indian sub-continent and Iran: Zürcher Hochschule für Angewandte Wissenschaften (ZHAW) (more info)
Every year, the Japan Society for the Promotion of Science (JSPS) offers fellowships to postdoctoral researchers interested in a stay of 12-24 months in Japan for research purposes. SNF acts as the nomination body and handles the evaluation process of applicants, at the end of which SNF recommends a selection of researchers to JSPS.