If they are defeated in this, the third attempt to derail the £400m plan, the Aberdeen Western Peripheral Route (AWPR) is likely to go ahead.
But William Walton of the group Road Sense said he was "optimistic" ahead of the two-day trial.
He said: "We will have to look at what the judgment says. I think the possibility of going to the European Court of Justice, that really is in the gift of the judges as to whether they think it is a part of European law that it needs further exploration and clarification. Unless that happens then it cannot go to the European Court of Justice and I don't think there is a human rights issue here, so I suspect we are not going to the European Court of Human Rights, in which case this would be the end of the process."
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The campaign group states it has come out of the "anger, bewilderment and sheer frustration" of people living to the west of Scotland and attacked the Scottish Government's decision to let it go ahead as "unfair".
But business leaders and some politicians have said the new road is vital for the economy in the north-east of Scotland.
Transport Minister Keith Brown said: "We are prepared and ready to defend the appeal so that we can get on and build this much-needed road as soon as possible."
(NE)
