The goal of the EU IST int. eu. grid project is to build middleware facilities which enable the execution of real-time and interactive applications on the Grid. Within this research, relevant support for the HEP application is provided by Virtual Organization, monitoring system, and real-time dispatcher (RTD). These facilities realize the pilot jobs idea that allows to allocate grid resources in advance and to analyze events in real time. In the paper we present HEP Virtual Organization, the details of monitoring, and RTD. We present the way of running the HEP application using the above facilities to fit into the real-time application requirements.