Bill Hawkes, 54, and 14-year-old Ciaran Hawkes were killed after their Mazda MX5 was involved in a collision with a Kia Optima on the A91 near Auchtermuchty.
Mr Hawkes and his son, who were from the Falkirk area, were travelling home from a classic car show.
Inquiries into the crash are continuing and police have asked any further witnesses to contact them.
A statement from the Hawkes family said: "Bill and Ciaran sadly died in a vehicle accident after attending a classic car show on Sunday. Their deaths are such a tragic loss.
"During their lives, both Bill and Ciaran touched so many people with their kindness, friendliness, thoughtfulness and generosity of spirit.
"They will be hugely missed by family and friends. The family is finding it extremely difficult to come to terms with this tragic sudden loss."
Police have said a man and boy killed in a road crash in Fife on Sunday were a father and son.