Officials from Russia and the European Union have begun wrestling with the issue of how the enclave's one million residents will be able to travel to the rest of Russia, once EU expansion has surrounded Kaliningrad.
The formal talks are aimed at finding a solution to the problem by the time the EU and Russia hold a summit in November.
The enclave will become an island in the expanded EU once its neighbours - Poland and Lithuania - have joined.
Residents of Kaliningrad - already blighted by economic, crime and pollution problems, fear they will become more cut off than ever.
Russia wants the residents to be allowed to travel freely through Poland and Lithuania to reach Russia.
But the two states are insisting that the travellers will need visas - a demand which Russia says is insulting.
The Brussels talks are trying to find a compromise.
The discussions are being chaired by Denmark, which currently holds the EU presidency.
The BBC's Caroline Wyatt in Moscow says the issue has become a matter of pride for Russia, although Kaliningrad itself is doing its best to persuade the EU that its economy and border security are improving so that Brussels need not fear illegal immigration or crime from across the border.