There are many different open source real-time operating systems (RTOS) available, and the use of open source software (OSS) for safety-critical applications is considered highly interesting by industrial domains such as medical, aerospace and automotive, as it potentially enables lower costs and more flexibility. In order to use OSS in a safety-critical context, however, evidence that the software fulfills the requirements put forth in a functional safety standard for the relevant domain is necessary. However, the standards for functional safety typically do not provide a clear method for how one would go about certifying systems containing OSS. Therefore, in this paper we identify some important RTOS characteristics and outline a methodology which can be used to assess the suitability of an open source RTOS for use in a safety-critical application. A case study is also carried out, comparing two open source operating systems using the identified characteristics. The most suitable candidate is then assessed in order to see to what degree it can adhere with the requirements put forth in the widely used functional safety standard IEC 61508.