Thieves rode off with two modified motorbikes after breaking in to a house in Carnoustie.
The Hondas – one of them a Fireblade with gold wheels – were later spotted in the Fintry and Whitfield areas of Dundee.
It is understood police pursued a balaclava-clad person on one of the stolen bikes but were unable to keep up as it dodged through the traffic.
Distraught owners Lynda Morton and Kenny Malcolm have urged anyone who has seen the bikes or has information which may help trace them to contact police.
Police Scotland confirmed it was investigating a break-in to a property in Carlogie Road, which occurred between 3pm and 4pm on Wednesday.
Cameras and equipment worth several thousand pounds and laptops were also taken.
Lynda said: “I had only gone out for an hour.
“When I drove up the road I saw the tail bag from my bike lying on the pavement outside my neighbour’s house.
“I looked up and the garage door was open and the bikes were gone.”
One of the motorbikes is a Honda CBR600F, mainly white and red.
The other is a 2013 Fireblade modified to look like a Fireblade SP. It is red, white and blue with gold wheels and was described as one-off.