Daniel and Liam Poole, from Burgess Hill, travelled to Malaga, Spain, on March 31, police said.
They hired a car when they got there but it has not been returned to the car hire firm.
Their family have not heard from them since April 1, police said, which is ‘out of character’.
A spokesman for Sussex Police said today (May 2): “British and Spanish police are working together to investigate the disappearance of father and son Daniel and Liam Poole after they travelled to Malaga, Spain, on March 31.
“The Surrey and Sussex Major Crime Team are now undertaking this enquiry and have resources already working with the Spanish authorities to find Daniel and Liam from Burgess Hill and investigate the circumstances of their disappearance.”
Detective Chief Inspector Emma Heater said: “We are working closely with the Spanish Police. One possibility that must be considered, as they have not contacted family or friends, is that they have come to harm.
“Their family are very concerned about them as they last heard from them on April 1, the lack of contact is out of character for the pair.
“The family are being supported by family liaison officers and are being kept informed.
“We know that Daniel and Liam hired a grey Peugeot 308 car when they got to Spain but this has not been returned to the car hire firm.
“We would like to hear from anyone who has seen them, the car or has any information about their whereabouts in Spain or any other location since March 31.”
Anyone who can assist with the investigation can report online or ring 101 quoting Operation Pheasant.