Adaptive Distributed Systems (ADSs) are distributed systems that can evolve their behaviors based on changes in their environments. In this work, we discuss security and propose security metrics issues in the context of ADSs. A key premise with adaptation of distributed systems is that in order to detect changes, information must be collected by monitoring the system and its environment. How monitoring should be done, what should be monitored, and the impact monitoring may have on the security mechanism of the target system need to be carefully considered. Conversely, the impact of implementation of security mechanism on the adaptation of distributed system is also assessed. We propose security metrics that can be used to quantify the impact of monitoring on the security mechanism of the target distributed system.