Extensive delays in cases such as the extradition of radical cleric Abu Hamza are a "source of real fury", the most senior judge in England and Wales said.
He was responding to a question about Hamza's extradition to the United States, which has again been put on hold pending a further hearing next week.
The Lord Chief Justice, Lord Judge, said: "I'm not going to comment about any individual case, but any case that takes eight years through a whole series of judicial processes to come to a conclusion - and you've made the point that it hasn't yet come to a conclusion - is a source of real fury to me," Lord Judge said.
"We really can't have cases taking that long to reach a conclusion. It's not fair to anybody. It's not right. And that's all I can really say about it."
The Lord Chief Justice went on: "The problem isn't that there isn't a limit on the number of appeals. The problem is that new points keep coming up and new points are taken and then they go through the process.
"What you need is a process in which all the points which need to be addressed are addressed once and then there is an appeal process and it comes to an end. Any case that takes eight years - unless there's some extraordinary explanation, like the parties don't want it, they're not in a hurry - is unacceptable."
Hamza's last-ditch bid in his long fight against extradition to the United States will be heard by the High Court next week. Two judges in London will also consider a challenge by a second terror suspect, Khaled Al-Fawwaz, next Tuesday. The men are seeking injunctions preventing their removal from the UK.
Pending the hearing of their applications by Sir John Thomas, President of the Queen's Bench Division, and Mr Justice Ouseley, interim injunctions have been issued preventing their removal.
The latest legal action came after Europe's human rights judges rejected a bid for an appeal by Hamza and four other terror suspects, paving the way for their extradition. A panel of five judges threw out their request to the Grand Chamber of the European Court of Human Rights.
Hamza, who was jailed for seven years for soliciting to murder and inciting racial hatred, has been fighting extradition since 2004. After the ruling in Europe, the Home Office said Hamza and the others would be "handed over to the US authorities as quickly as possible".