As multicore processors are becoming increasingly common everywhere, the future computing systems and devices are becoming inevitably concurrent. Also, on the applications side, automation is steadily infiltrating into everyday life, and hence, most software systems are becoming increasingly complex and concurrent. As a result, recent developments and projections indicate that we are entering into the era of concurrent programming. Synchronizing asynchronous concurrent processes in accessing a shared resource is an important issue. Among the synchronization issues, mutual exclusion is fundamental. Solutions to most higher level synchronization problems rely on the assurance of mutual exclusion. Several algorithms with varying characteristics are proposed in the literature to solve the mutual exclusion problem. This paper presents two new algorithms to solve the mutual exclusion problem. The algorithms are simple and have many nice properties.