Explorative Location-based Applications (eLBA) define a new class of applications that rely on both positioning (i.e. location information) and georeferenced information in addition to a flexible and efficient system infrastructure that supports a mobile and ubiquitous usage. In this paper we define first a modeling framework to design eLBAs that builds on the concept of tasks as a very valuable system/user interaction and application structuring concept. In addition, we report on a system framework, the Nexus platform, that efficiently provides access to georeferenced information and positioning information. Our sample application, the NexusRallye, is used to exemplify important aspects of our solution platform and to show its advantages as compared to other approaches.