Some students have been applying for money after starting their courses
The Student Awards Agency for Scotland (Saas) had to take on extra staff to cope with "higher volumes of applications than usual" this year.
It said thousands of people applied at a late stage for financial support, in some cases after courses had begun.
It has processed 117,500 applications out of 135,784 received to date.
It stresses the system is not affected by the delays in loan and grant payments to English students, though there are ongoing postal disruptions.
These might mean it was taking longer than normal to receive any documents people had sent in support of their applications and for students to receive their award letters, it said.
"If you still have not heard from Saas 28 days after making your application, or if you are concerned, please check the status of your application at www.saas.gov.uk before contacting the agency by e-mail."
The thousands who applied late are being told their applications will be processed as soon as possible.
In the meantime people suffering hardship should approach their college or university for assistance from their discretionary funds.
A 10% rise in applications had been predicted for this year by the Scottish government following its reforms to the student support system.
This is likely to have been boosted by the impact of the recession and the relative lack of jobs as an alternative to higher education.
The Saas has said it has been meeting its target of processing applications within 21 days of receipt in almost all cases.
It has made available more telephone lines, employed additional staff, put in extra facilities to handle visitors to its office and has been working longer hours.
Some people have been worried by reports of the widespread problems affecting tens of thousands of students, especially in England, whose applications are handled by the separate - albeit Scottish-based - Student Loans Company.
"Because Saas calculates the amount of loan they will receive, Scottish students are not currently affected by the delays in student loan payments being experienced by students in England," the Saas said.
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