There are two major requirements for any surveillance application of Wireless Sensor Networks (WSN) — coverage and connectivity. In the design of any algorithm for WSN, the major constraint is limited battery life time of the sensor nodes. Most of the existing work on combined problem of coverage and connectivity either require the clocks of the nodes to be synchronized or require exact location information of the nodes to be known. In this paper, we present an Asynchronous Algorithm which is Energy Efficient and provides integrated Coverage and Connectivity, called (AAEECC). Our algorithm does not require clock synchronization of nodes at any stage neither does it require exact location information of the nodes. It is low cost, fully distributed and scalable. In the following, we discuss the approach used. First, we build a minimum hopcount graph for connectivity. Second, we propose a scheduling algorithm for providing desired coverage. Third, we define a fault tolerant connectivity maintenance algorithm (FTCM) to re-ensure connectivity as network may become disconnected due to scheduling.