This paper discusses an approach for supporting soft real-time periodic tasks in Linux on performance asymmetric multicore platforms (AMPs). Such architectures consist of a large number of processing units on one or several chips, where each processing unit is capable of executing the same instruction set at a different performance level. We discuss deficiencies of Linux in supporting periodic real-time tasks, particularly when cores are asymmetric, and how such deficiencies were overcome. We also investigate how to provide good performance for non-real-time tasks in the presence of a real-time workload. We show that this can be done by using deferrable servers to explicitly reserve a share of each core for non-real-time tasks. This allows non-real-time tasks to have priority over real-time tasks when doing so will not cause timing requirements to be violated, thus improving non-real-time response times. Experiments show that even small deferrable servers can have a dramatic impact on non-real-time task performance.