Cloud computing Web systems are today the most important part of the Web. Many companies transfer their services to the cloud in order to avoid infrastructure aging and thus preventing less efficient computing. Distribution of the load is a crucial problem in cloud computing systems. Due to the specifics of network traffic, providing an acceptable time of access to the Web content is not trivial. The utilization of the load distribution with adaptive intelligent distribution strategies can deliver the highest quality of service, short service time and reduce the costs. In the article, a new, two-level, intelligent HTTP request distribution strategy is presented. In the process of designing the architecture of the proposed solution, the results of earlier studies and experiments were taken into account. The proposed decision system contains fuzzy-neural models yielding minimal service times in the Web cloud. The article contains a description of the new solution and the test-bed. In the end, the results of the experiments are discussed and conclusions and presented.