In this paper the first results on the Online Dial-A-Ride Problem with Time-Windows (ODARPTW for short) are presented. Requests for rides appearing over time consist of two points in a metric space, a source and a destination. Servers transport objects of requests from sources to destinations. Each request specifies a deadline. If a request is not be served by its deadline, it will be called off. The goal is to plan the motion of servers in an online way so that the maximum number of requests is met by their deadlines. We perform competitive analysis of two deterministic strategies for the problem with a single server in two cases separately, where the server has unit capacity and where the server has infinite capacity. The competitive ratios of the strategies are obtained. We also prove a lower bound on the competitive ratio of any deterministic algorithm of $\frac{2-T}{2T}$ for a server with unit capacity and of $\frac{2-T}{2T} \lceil \frac{1}{T} \rceil$ for a server with infinite capacity, where T denotes the diameter of the metric space.