Background: Our previous phase 2, open-label study of 11 infants and young children with life-threatening perinatal or infantile hypophosphatasia showed 1 year safety and efficacy of asfotase alfa, an enzyme replacement therapy. We aimed to report the long-term outcomes over approximately 7 years of treatment. Methods: We did a prespecified, end of study, 7 year follow-up of our single-arm, open-label, phase 2 trial in which children aged 3 years or younger with life-threatening perinatal or infantile hypophosphatasia were recruited from ten hospitals (six in the USA, two in the UK, one in Canada, and one in the United Arab Emirates). Patients received asfotase alfa (1 mg/kg three times per week subcutaneously, adjusted to 3 mg/kg three times per week if required) for up to 7 years (primary treatment period plus extension phase) or until the product became commercially available; dosage adjustments were made at each visit according to changes in the patient's weight. The primary objectives of this extension study were to assess the long-term tolerability of asfotase alfa, defined as the number of patients with one or more treatment-emergent adverse events, and skeletal manifestations associated with hypophosphatasia, evaluated using the Radiographic Global Impression of Change (RGI-C) scale (−3 indicating severe worsening, and +3 complete or near-complete healing). Respiratory support, growth, and cognitive and motor functions were also evaluated. All efficacy and safety analyses were done in all patients who received any asfotase alfa (full-analysis population). This study and extension phase are registered with ClinicalTrials.gov, number NCT01205152, and EudraCT, number 2009-009369-32. Findings: 11 participants were recruited between Oct 6, 2008, and Dec 4, 2009. Ten patients completed a 6 month treatment period and entered the extension phase; nine received asfotase alfa for at least 6 years and completed the study, with four being treated for more than 7 years. Skeletal healing was sustained over 7 years of treatment; all evaluable patients had RGI-C scores of at least +2 at year 6 (n=9; median score +2·0 [range 2·0–3·0]) and year 7 (n=7; median score +2·3 [2·0–3·0]). No patient who completed the study required respiratory support after year 4. Weight Z scores improved to within normal range from year 3 to study end; length or height Z scores improved but remained below normal. Age-equivalent scores on gross motor, fine motor, and cognitive subscales of the Bayley Scales of Infant and Toddler Development also improved. All 11 patients had at least one treatment-emergent adverse event. The most common adverse events were pyrexia (eight [73%] of 11 patients), upper respiratory tract infection (eight [73%]), craniosynostosis (seven [64%]), and pneumonia (seven [64%]). Serious adverse events related to asfotase alfa occurred in three (27%) patients (severe chronic hepatitis; moderate immediate post-injection reaction; and severe craniosynostosis with severe conductive deafness). Interpretation: Patients with perinatal or infantile hypophosphatasia treated with asfotase alfa for up to 7 years showed early, sustained improvements in skeletal mineralisation. Respiratory function, growth, and cognitive and motor function also improved, and asfotase alfa was generally well tolerated. Funding: Alexion Pharmaceuticals, Inc.