This paper presents a system framework to support continuous nearest surrounder (NS) queries in moving object environments. NS query finds the nearest objects at individual distinct angles from a query point. This query distinguishes itself from other conventional spatial queries such as range queries and nearest neighbor queries by considering both distance and angular aspects of objects with respect to a query point. One of NS query applications is to monitor the nearest objects around an observation point. In our framework, a centralized server is dedicated to collect object location updates, to determine affected NS queries of each object location update, to compute the incremental result change of affected queries and to deliver result updates to corresponding interested users/applications that initiate the queries. In particular, we propose algorithms namely, safe region formation and partial query evaluation, that can significantly improve the system performance. Through simulations, we validate our proposed algorithms over a wide range of settings.