The raiders stole house keys, a computer tablet and a mobile phone from the St Vigeans Road flat between 18:00 on Tuesday and 07:30 on Wednesday.
Thieves then returned to steal four gent's watches from the same property at about 01:00 on Thursday.
Officers have appealed for anyone who was in the area at the time to come forward.
Police are hunting thieves who targeted an Arbroath flat twice in the space of two days.