Around 600 people arriving on early-morning flights at Glasgow Airport had to queue until the problem was resolved.
Glasgow Airport said that those affected were on two flights from Greece and one from Egypt.
The Border Force said that security was not compromised.
The problem lasted two to three hours and was resolved by 6.30am.
A force spokesman said: “A power failure in the Border Force computer systems at Glasgow airport this morning led to regrettable delays for some passengers. The problem was quickly fixed, full checks were carried out on all passengers and border security was not compromised.”