An arsonist caused damaged estimated at between £20,000 and £40,000 to a shop in Portslade.
The same person is believed to be responsible for another fire near by in Mile Oak just over an hour earlier.
Both fires were started on Sunday evening (8 June).
The fire which damaged a shop was started in a wheelie bin in Valley Road at about 7.30pm.
Efforts were made to tackle the fire but it had spread to the Mulberry convenience store roof and storeroom before East Sussex Fire and Rescue Service crews arrived.
Sussex Police said: “Police are linking this blaze to another deliberate fire in Graham Avenue, Portslade, at 6.20pm on Sunday where a gate and pile of rubbish were set alight. It was put out by fire and rescue officers.”
Detective Sergeant Simon Dunn said: “These are both being linked because they are close in terms of location and there was considerable damage caused at the Mulberry store.
“Fortunately no one was hurt. We want to hear from anyone who saw anything suspicious in these areas on Sunday evening.”
Anyone with information is asked to phone Sussex Police on 101 or email 101@sussex.pnn.police.uk.
