Citizens’ rights in each other’s nations are considered the first issue that both sides must settle.
Many details have not yet been worked out and further negotiations are expected.
EU leaders have agreed that the post-Brexit locations of key bank and medical agencies currently based in London would be decided by November.
Talks on Britain leaving the European Union began Monday with both sides saying they will focus first on an orderly withdrawal.
EU officials do acknowledge that the agreements to be reached before Britain leaves in March 2019 can only be concluded as a whole package simultaneously.