The limits of soft safety regulation: Does successful work with safety culture require SMS implementation?

•The Swedish Transport Agency defined contributing to a high safety culture in transport companies as a key element in its regulatory strategy.•This study examines how this strategy was received and enacted by regulators and companies within each transport sector, and factors influencing this.•We discuss what a regulatory agency can accomplish through a safety culture strategy.•A key question is whether safety management requires a sequential, or evolutionary development.•This means that companies must implement well-functioning safety management systems before being organisationally mature enough to work successfully with safety culture.•Our results seem to support this assertion.