It has ground to a halt because the US has blocked the appointment of new judges.
A minimum of three are needed and today there is just one in place.
The Appellate Body has the final say on disputes that cover billions of dollars of international trade and its decisions are supposed to be binding.
However, now that it has ceased to function and can't take on new cases Mr Azevedo conceded that "significant changes in the dispute settlement mechanism" will be needed and that "intensive consultations" will start immediately.
These are likely to include "looking at issues like how fast can the disputes settlement work", he said in a BBC interview
Those changes are being demanded by President Trump's administration in Washington. Their argument is that the WTO has treated the United States unfairly. Some of their criticisms are shared by other countries but others are not. Despite this Mr Azevedo says that Donald Trump's tenure as US president is not a barrier to reaching a solution.
"It's whether we can find fixes that everybody can live with".
He adds that, "these are extremely complex conversations and negotiations and very political in nature, so we have to understand this is not something that is going to be solved overnight, just like that".
Mr Trump's role is disputed by Professor James Bacchus, a former chairman, or chief judge, of the WTO Appellate Body as well as a former US trade negotiator. He told the BBC there is "little chance of resolving this while Donald Trump is still president in a way that will continue to preserve the independence and impartiality of the Appellate Body and the rest of the WTO dispute settlement system".
He says that whilst the US has won the vast majority of cases it has bought at the WTO it has repeatedly violated the trade remedies imposed on it by the organisation.
Professor Bacchus says that many of the US claims against the WTO are "trumped up".
One area that particularly grates in Washington is dumping when a foreign supplier sells goods abroad more cheaply than at home. The US and others have used a disputed method for assessing whether goods have been dumped and how much the price is below what it should be.
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