Sustainability is becoming more and more the key challenge for organisations. Sustainability depends on internal and external characteristics of the organisation that should or must be preserved within the time and depends on the definition of what is a suitable state of the system (organisation and its environment) within medium and long terms as safety can be seen as feature of sustainability. The concept of sustainability is a key concept for safety researchers and practitioners. The reverse is true as safety concepts are useful to think sustainability which is still rather new. They share common research grounds on management and organisations sciences. In France, as exemplary organisations, public organisations are working on issues related to both the assessment and governance of sustainability. In this paper we propose a "proactive-based assessment" designed to measure an organisation's ability to govern and achieve sustainability. The proposed assessment method relies on three new concepts: "critical capital"; Highly Sustainable Organisation (HSO), and learning stages within an HSO. Although there are some elements of unpredictability in complex systems, sustainability for an organisation is based at least on its ability to learn and adapt. There are different ways of conceiving sustainability for public organisations. Even though there is no consensus on the way public organisations are conceived, there is still a philosophical and political agreement on the need for more sustainability. However, it is still unclear and sometimes not even pointed "what should be sustained for public organisations?". We suggest that the "critical capital" is characterised by internal and external aspects of the organisation that should be preserved within the time such as (i) the way of functioning of the organisation, (ii) the way the missions are performed or exercised by the organisation to meet what is contextually referred as being of public and common needs and (iii) the "organisational memory" that represents the identity of the public organisation and the assets of the public organisation. The term "Capital" does not refer to its definition in economy but to its given definitions in sociology (see for example Ferragina, 2010) and ecology (see for example Jansson, 1994). Criticality is fixed "according to the way public service is conceived, to the contextual constraints (such as economical, environmental, social, cultural and ethical) and according to the degree and the nature of threats (natural and manmade hazards). We suggest that organisational sustainability is the ability of the system to preserve and to maintain, within the time, a critical capital and to adapt to its ecosystem. Accordingly, a loss of organisational sustainability indicate whether the organisation is prone to shift to an undesirable organisational state that would decrease the ability or even cease to provide services to the ecosystem and to maintain its identity. In other words, it is an organisation that loses part of its critical capital. Accordingly, we have proposed a development stage model to make explicit the way we have observed in these organisations a common progression in the initiatives they have taken to address sustainability challenges and build learning and innovation capabilities. The three concepts arise from a four years investigation and observation of more than 60 public organisations in France and the coordination, at a national level, of the French working group on "governance of public organisations" that end up with the publication of four national guidelines in March 2013