Equatorial Guinea's President Teodoro Obiang Nguema is in Harare for talks with President Robert Mugabe.
President Obiang (l) promised to help Zimbabwe on a visit in 2006
Correspondents say the dialogue is likely to focus on Zimbabwe's need for fuel, which Equatorial Guinea - as an oil producer - could supply.
The dialogue between the two African heads of state began on Wednesday.
Zimbabwe, which is currently suffering severe economic difficulties, needs to spend around $130m (£64m) a month on oil imports.
Also on the agenda is likely to be the possible extradition of the man who led an attempted coup against President Obiang, the former British army officer Simon Mann, who is currently imprisoned in Zimbabwe.
President Obiang is in the country to officially open the Harare Agricultural Show on Friday.
Human rights organisations have accused President Obiang of running a dictatorship responsible for gross human rights violations. Mr Mugabe faces similar accusations.