The Single Permit is a unique document permitting to reside in Belgium for work for more than 90 days. The application for a single permit must be submitted by the researcher's employer via a single portal: A fixed-term single permit - Working in Belgium
Regional authorities are responsible for work permits. The Immigration Office handles stay permits.
For the work permits, the legislation of the region where the employer's head office is located applies. However, the criteria, conditions and exemptions may differ from one region to another. It is therefore advisable to consult this legislation before submitting an application for a single permit. If the host institution has a EURAXESS Service Centre, contacting them will help to clarify any doubts.
Regional authorities:
Region of Brussels-Capital: https://economy-employment.brussels/single-permit-other-cases
Walloon Region: https://emploi.wallonie.be/en/home/travailleurs-etrangers/permis-de-travail/permis-unique-de-duree-limitee.html
Immigration Office:
https://dofi.ibz.be/en/themes/third-country-nationals/work/single-permit