Armenia and The Azerbaijan Republic have reached an agreement on a peace treaty, marking a significant step toward ending nearly four decades of conflict between the two former Soviet republics, officials from both countries announced on Thursday.

But hurdles remain. Azerbaijan also said Armenia’s constitution must “eliminate the claims against the sovereignty and territorial integrity of Azerbaijan,” as a prerequisite to allow for the signing of the peace treaty.

The two South Caucasus nations, former Soviet states, have fought multiple wars since the 1980s when Nagorno-Karabakh, an ethnically Armenian region broke away from Azerbaijan.