Cloud service security management in cloud computer environment uses a first computer cloud entity with first security capabilities and under security management coordinated by a first security management service point in compliance with predefined first security requirements. Security management of a second computer cloud entity is coordinated by a second security management service point in compliance with predefined second security requirements. In the managing of the security of the cloud service in the cloud computer environment: a trusted relationship is established between the first and second security management service points, general security requirements for the cloud service are obtained; and a first security policy is defined for the first security management service point, based on the general security requirements for the cloud service, the first security capabilities and the first security requirements, for the running of the cloud service by the first computer cloud entity.