Abstract : Many scientific applications are described through workflow structures. Due to the increasing level of parallelism offered by modern computing infrastructures, workflow applications now have to be composed not only of sequential programs, but also of parallel ones. Cloud platforms bring on-demand resource provisioning and pay-as-you-go payment charging. Then the execution of a workflow corresponds to a certain budget. The current work addresses the problem of resource allocation for non-deterministic workflows under budget constraints. We present a way of transforming the initial problem into sub-problems that have been studied before. We propose two new allocation algorithms that are capable of determining resource allocations under budget constraints and we present ways of using them to address the problem at hand.