Finance director Clive Timms, 47, has resigned "for personal reasons", and the ROH is about to lose its head of finance, David Pilcher, who has been made redundant.
The departures coincide with one of the most turbulent points of the London opera house's history, just as it is about to start a redevelopment that, including its travelling costs, will cost a total of pounds 213m.
The ROH, which became the centre of a controversy when it was promised pounds 78m in lottery grants, has to raise an equivalent amount through sponsorship from businesses and individuals to qualify for the award.
A spokeswoman yesterday said that she could not say how the resignations would affect the institution's fundraising plans. "I think until we have information on the structure of the finance department after Clive Timms, it really is difficult to comment," she said.
Although she would not comment on the reasons behind his departure, Mr Timms' resignation is said to have followed an internal row over the ROH's projected budget for 1997-98, which the Arts Council proposed should be cut back by about pounds 3m.
The ROH's current problems have been made more pressing because building work on the redevelopment has already been started.
The House is due to close, during the summer next year, and is still attempting to finalise its plans for its first year as a travelling house.
The ROH will be setting up in a temporary home in London, probably at the Barbican Centre, and the Royal Ballet will be touring.