Caching is a key component for Content Distribution Networks and new Information-Centric Network architectures. In this paper, we address performance issues of caching networks running the RND replacement policy. We first prove that when the popularity distribution follows a general power-law with decay exponent α > 1, the miss probability is asymptotic to O( C1-α) for large cache size C. We further evaluate network of caches under RND policy for homogeneous tree networks and extend the analysis to tandem cache networks where caches employ either LRU or RND policies.