Many animals exhibit behavioural syndromes-consistent individual differences in behaviour across two or more contexts or situations. Here, we present adaptive, state-dependent mathematical models for analysing issues about behavioural syndromes. We find that asset protection (where individuals with more 'assets' tend be more cautious) and starvation avoidance, two state-dependent mechanisms, can explain short-term behavioural consistency, but not long-term stable behavioural types (BTs). These negative-feedback mechanisms tend to produce convergence in state and behaviour over time. In contrast, a positive-feedback mechanism, state-dependent safety (where individuals with higher energy reserves, size, condition or vigour are better at coping with predators), can explain stable differences in personality over the long term. The relative importance of negative- and positive-feedback mechanisms in governing behavioural consistency depends on environmental conditions (predation risk and resource availability). Behavioural syndromes emerge more readily in conditions of intermediate ecological favourability (e.g. medium risk and medium resources, or high risk and resources, or low risk and resources). Under these conditions, individuals with higher initial state maintain a tendency to be bolder than individuals that start with low initial state; i.e. later BT is determined by state during an early 'developmental window'. In contrast, when conditions are highly favourable (low risk, high resources) or highly unfavourable (high risk, low resources), individuals converge to be all relatively bold or all relatively cautious, respectively. In those circumstances, initial differences in BT are not maintained over the long term, and there is no early developmental window where initial state governs later BT. The exact range of ecological conditions favouring behavioural syndromes depends also on the strength of state-dependent safety.