Cloud computing services have been increasingly considered by businesses as a viable option for reducing IT expenditure. However, there are often associated problems with unmanaged accountability. This paper first analyses the accountability properties of a cloud service and then proposes the accountable cloud service (ACS) model to address those problems. In addition, the authors argue that from an accountability perspective a cloud service is a proactive system that needs to be modeled differently from the traditional reactive systems. They extend traditional structural operational semantics to cater for modeling of actors as well as scenarios of inaction and exception in state transitions. This leads to the creation of a new form of a process algebra called Accountable Process Algebra (APA). They also propose an Obligation Flow Diagram (OFD) as a simple method for conflict resolution and verification for the ACS model. The ACS model enables obligation specification, validation, decomposition, machine-interpretation, monitoring and reasoning, and ultimately facilitates accountability in cloud service consumption. Using Amazon S3 service as a case study, they show how to address those known accountability problems by using our ACS model. Finally the authors discuss the applicability of their model to cloud services in general.