Most Scottish universities are full, with no places for prospective students who have fallen short on exam grades.
A total of eight out of Scotland's 15 universities say they will not be taking candidates through the annual "clearing" process.
Those who have achieved the required results are safe, but five universities cannot take extra students.
The recession caused a huge rise in demand for places in the tough jobs market.
However, new figures released by administrative body Universities Scotland said there were still vacancies on more than 300 university courses.
But the gaps are concentrated in four institutions - Abertay in Dundee, the University of the Highlands and Islands, the University of the West of Scotland, formerly Paisley University, and at the Scottish Agricultural College.
The Scottish government has given universities more than £1bn this year, but many have not been not been able to cope with extra demand, and some have reported increases of up to 41% in applications.
More than 2,000 places were offered through clearing last year - but that figure is expected to drop to several hundred this time.
Rachel Sandison, head of admissions at Aberdeen University, which is for the first time not offering clearing places, said: "The University of Aberdeen has enjoyed a significant increase in applications this year and, as a result, will have no vacancies through clearing."
Glasgow Caledonian, Heriot-Watt, Queen Margaret and Strathclyde universities are in the same position, while Glasgow, Edinburgh and St Andrews have not offered places through clearing for several years.
A spokesman for Universities Scotland, said: "This is definitely a very tough year for anyone who is trying to find a university place through clearing because the rise in applications mean there are very few places left."
Prospective students have been urged to check the Ucas website for universities that are holding vacancies.
A government spokesman, said: "In the current economic climate, we recognise there are more people considering applying for higher education courses and we will obviously be continuing to work with Ucas, Scottish Funding Council and the sector to closely monitor demand for places next year."