In a joint statement, they said a series of working groups would be set up to deal with key sticking points.
The leaders of the five main parties at Stormont will also hold weekly meetings with the NI Secretary and Tanaiste (Irish deputy PM) to “take stock” and set the agenda.
The talks involving the NI parties and governments got under way on Tuesday afternoon.
The plans for the five strands are as follows:
1) Programme for Government
2) Transparency, accountability & operation of Executive
3) Petition of concern
4) Rights, language and identity
5) Sustainability, stability & operation of the institutions
It is the first fully-fledged talks process since negotiations collapsed in February 2018.
The North of Ireland has been without a devolved power-sharing government for more than two and a half years, after the DUP and Sinn Féin split in a bitter row over the cash-for-ash RHI scandal.
There have been several failed talks processes since January 2017.
Last month, the British and Irish governments agreed to convene a new set of talks from May 7 which they insist will be short and focused.
In their statement issued after meeting the Stormont party leaders on Tuesday, they said Taoiseach Leo Varadkar and British Prime Minister Theresay May will review progress at the end of May.
There will be the weekly round-table meeting involving party leaders and the working groups will deal with several key issues.
They will be made up of three representatives from each of the five parties in the talks, and representatives from the British and Irish governments will advise them.
Strand one will be chaired by the current head of the NI Civil Service David Sterling.
The second strand will be overseen by Hugh Widdis, departmental solicitor and former assembly legal counsel.
Strand three, which is regarded as toughest as it deals with rights/marriage and the Irish language, will be chaired by former culture department permanent secretary, Paul Sweeney.
Ex-NI civil service boss Sir Malcolm McKibbin will look after Strand Four.
And Strand Five will be led by the permanent secretary of finance, Sue Gray.
Several parties at Stormont have called for the reform of the petition of concern mechanism – it is effectively a Stormont veto which the DUP used to block same-sex marriage.
The talks were announced by the British and Irish governments after the murder of journalist Lyra McKee.
At her funeral in St Anne’s Cathedral, politicians came under pressure to solve the Stormont impasse.
The talks are beginning just days after council elections, which saw a surge of support for smaller parties not aligned to either unionism or nationalism.
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