In the latest in a series of papers setting out its Brexit negotiating plans, the government will say disputes need to be resolved in a clear and sensible way, saying it is determined to agree new arrangements. This will be crucial for both UK and EU citizens and businesses that buy and sell across borders, it says.
The future partnership paper on civil judicial cooperation follows publications on the customs union, the Irish border and the trading of goods after Brexit.
A paper on the key issue of the role of the European Court of Justice is expected on Wednesday. The publications are part of the UK government's attempts to persuade the EU to move the Brexit talks on to the next phase, which will include trade negotiations.
Brussels says this cannot happen until sufficient progress has been made on citizens' rights, the UK's divorce bill and the Northern Ireland border.
Labor accused the government of publishing bland, non-committal papers as a smokescreen to mask their failure to make any meaningful progress on the initial negotiations.
The EU has already published its own position paper on judicial co-operation. Papers from the UK side will promise to build on the existing foundation of co-operation and respect for the rule of law with the EU.
It will propose a replacement for the UK's membership of the EU's judicial co-operation system, which sets out how cross-border disputes are handled.
The system decides which country's legal system takes the lead, and means member states respect each other's judgments.
Lawyers and MPs have warned that the UK's status as a global legal centre for commercial contracts could come under threat from rival countries unless clear arrangements are put in place for after Brexit.
Pro-EU campaign group Open Britain said the government had made an appalling error by ruling out a role for the European Court of Justice in regulating disputes.