As part of their appeal, officers have released CCTV images of people they want to speak to in connection with the incidents.
Insp Gary Ancell said: “The officers investigating these ten cases have followed a number of lines of enquiry and circulated these images on police intelligence systems to try and get names for these people, but to no avail so far.
“Now we are asking members of the public to help identify them. If you know any of these ten people and can tell us who they are, then we want to hear from you.”
Image 1 - Angmering
The man in image 1 is suspected of stealing a cycle from Angmering rail station between 9am and 9.15pm on Monday, June 4.
Image 2 - Barnham
Image 2 shows a group of youths believed to have taken a cycle from racks at Barnham rail station sometime between 12pm on Monday, June 25 and 1pm on Wednesday, June 27.
Image 3 - West Worthing
Officers want to speak to the man in Image 3 after a bike secured in a rack at West Worthing station was stolen between 8pm and 11.40pm on Wednesday, June 13.
Image 6 - Worthing
Officers want to identify the man in image 6 following the theft of a bicycle from Worthing rail station between 9am on Saturday 14 July and 11.45pm on Sunday, July 15.
Image 9 - Worthing
Officers are asking the public to help identify the man in image 9 after a bicycle locked in a shelter outside Worthing station was stolen between 7.30am and 5pm on Thursday, July 5.
Insp Ansell added: “Sadly bicycles are a popular target for thieves but there are lots of things people can do to make sure their property is adequately marked and secured.
“It’s important to remember to register your bike and ensure a solid lock is used to secure it. If a bike is adequately marked, it makes it much easier to identify and therefore helps reduce the risk of becoming a victim of bike theft.”
Anyone with any information about the incidents or who recognises one of the people pictured in the images should contact British Transport Police on Freefone 0800 40 50 40 quoting reference B8/LSA of 11/10/12, quoting the image number.