6 infants (index cases) from five different families had a near-miss sudden infant death syndrome event between 3 and 12 weeks of age and had polygraphically documented apnoeas during sleep. 4 of their siblings had died of SIDS. The index cases, their 4 living siblings, 10 parents, and 8 grandparents underwent respiratory studies during sleep. All the adults and 3 index cases had cephalometric X-rays. 2 index cases underwent volume computerised tomographic scans when awake and during sleep. Index cases had mixed and obstructive sleep apnoea. Several family members had obstructive sleep apnoea; cephalometric X-rays also showed small upper airways, particularly behind the base of the tongue. A small posterior airway at the level of the tongue may be a familial risk factor for apnoea of infancy.