They were named as Robert Roche, 36, from Hove, Sussex, a boy aged three and a girl aged 18 months.
They set off from their home at 09:00 BST to go to a day nursery in nearby Holland Road but did not arrive.
Police were called at 17:30 when family members realised that they had not returned home.
Mr Roche is described as white, 5ft 10in (1.78m), stocky, with dark hair.
His children are three-year-old Joey and 18-month-old Betsy, who was in a very distinctive black "Bugaboo donkey stroller" buggy with a pink hood. There is also a step and a "saddle" by the handle bar.
Det Insp Mick Jones from Sussex Police said: "We are searching the local area and are keen to hear from anyone who has spotted Robert and his children.
"If you see them or know where they might be, please let us know right away on 101 or 999, quoting serial 1053 of 14/08.
"We also ask Robert to get in touch with us so that we can arrange to meet and confirm that he and the children are ok.
"We are not treating the disappearance as suspicious at this stage but it has not happened before and we are naturally very concerned for Robert and especially for his children."
Police and family are concerned for the welfare of a man and his two small children who have not been seen since Monday morning.