In 2009 the US Federal Aviation Administration (FAA) introduced a slow growth approach for certifying composite and adhesively-bonded structures. This approach requires that delamination or disbond is slow, stable and predictable under cyclic-fatigue loads. The present paper addresses the challenge of developing a methodology capable of enabling this approach to certification to be implemented. To this end we have examined the growth of disbonds from small naturally-occurring material discontinuities in adhesively-bonded structures. It is shown that, for the examples studied, the disbond growth histories can be accurately computed using a form of the Hartman and Schijve variant of the NASGRO crack-growth equation. It is also shown that the scatter in the disbond growth histories can be captured by allowing for small changes in the fracture-mechanics threshold term. These findings suggest that the Hartman and Schijve variant of the NASGRO crack-growth equation has the potential to address the ‘slow growth’ approach to certifying composite/bonded structures and bonded repairs outlined in the US FAA Airworthiness Advisory Circular No: 20-107B.