A continuous k nearest neighbor (cKNN) query is a query that continuously returns a set of k nearest moving objects (mobile hosts) to a given query point. For example, report three nearest moving sensors to a given location continuously. Most existing research efforts focus on centralized solutions. In a mobile peer-to-peer network (M-P2P), a centralized approach incurs expensive communication cost. In this paper, we propose Safe-Time —a distributed solution for cKNN given a stationary query point for M-P2P. The two key features are as follows. 1) Actual execution of a cKNN query is not needed during a safetime period since the query result is guaranteed to remain the same during this period. 2) Once the safe-time expires, execution of a cKNN query involves only objects in a circular band of width equal to the estimated distance between the kth and the k+1th nearest neighbors. To further reduce communication cost for dense queries, we introduce Unite-Safe-Time that executes one virtual query derived from nearby queries instead of executing each of them separately. Our simulation result shows that the proposed distributed solutions outperform a centralized solution under a range of conditions. Safe-Time incurs up to 2/3 less communication cost compared to a centralized solution. Unite-Safe-Time shows up to 1/3 less cmmunication cost than Safe-Time in our study.