David and Allison Hartley's four sons, aged between four and 12, are all suffering from a rare genetic disease affecting their immune system.
Only a full bone marrow transplant will give the boys a normal life expectancy.
They have launched an appeal to find a suitable donor, through the Anthony Nolan Bone Marrow Trust.
Breakfast talked live to the Hartley family.
The Hartley's sons are suffering from an extremely rare condition, called X-linked lymphoproliferative disease (XLP), which was only discovered in 1999.
Sufferers do not usually live into their teens, but a bone marrow transplant can give them normal life expectancy.
Only 100 people in the world have so far been diagnosed with XLP, which affects only boys.
Allison has recently learned that she is a match for their eldest son, Joshua, but the family still need a tissue match for the other three boys.
At 12, Joshua is already suffering from acute anaemia caused by XLP. Ten year old Nathan has lymphoma.
The family hope to find a match through the Anthony Nolan Trust, which maintains the UK's largest register of bone marrow donors.
The Trust has 350,000 volunteers on its books, and is particularly keen to recruit more men, because women cannot donate within two years of a pregnancy.