A mother from Newark is wanted by police on suspicion of abducting her sons, Nottinghamshire Police has confirmed.
Samantha Baldwin, who was reported missing with her sons Dylan Madge, 6, and Louis Madge, 9, since Monday, is said to have no legal custody of them.
Officers believe they are together. It is believed they could be in Lincolnshire.
Samantha was last seen alone near Nottingham city centre at around noon on Monday. Neither she nor the boys have been seen since.
Officers have made two arrests in relation to the disappearance of the mother and two boys. A 62-year-old woman and a 36-year-old woman were arrested on suspicion of assisting an offender and have since been released on bail.
Superintendent Rich Fretwell said: “An investigation into the circumstances is well under way and we have a large amount of resources working around the clock to locate Dylan and Louis. Our priority at the moment is to locate them safe and well.
“We are now appealing for the return of Dylan and Louis and any information about the whereabouts of them and their mother, Samantha.”
Samantha is described as being 5ft 7ins tall, of a slim build, with shoulder-length, highlighted blonde hair and green/blue eyes. She was last seen wearing a red knee-length coat from Mango but may have changed her clothing since.
Louis is described as having collar-length straight fair hair, a fair complexion and blue eyes.
Dylan is described as having collar-length straight dark brown hair, a tanned complexion and brown eyes.
Officers do not have a description of the clothing the boys were last seen wearing.
A police spokesman said: “In the last 24 hours, we have seen thousands of messages of support and we have been overwhelmed by members of the public offering their help. We do not underestimate just how important information from the public is and we would like to say thank you for this continued support.”
Anyone with information of their whereabouts is urged to call Nottinghamshire Police on 101 urgently, quoting incident number 332 of March 27.