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The World Wide Web (or Web for short) is the largest client-server computing system commonly available, which is used through its widely accepted universal client (the Web browser) that uses a standard communication protocol known as the HyperText Transfer Protocol (HTTP) to display information described in the HyperText Markup Language (HTML). The current Web computing model allows the execution of server-side applications such as Servlets and client-side applications such as Applets. However, it offers limited support for another model of network computing where users would be able to use remote, and perhaps more powerful, machines for their computing needs. The client-server model enables anyone with a Web-enabled device ranging from desktop computers to cellular telephones, to retrieve information from the Web. In today's information society, however, users are overwhelmed by the information with which they are confronted on a daily basis. For subscribers of mobile wireless data services, this may present a problem. Wireless handheld devices, such as cellular telephones are connected via wireless networks that suffer from low bandwidth and have a greater tendency for network errors. In addition, wireless connections can be lost or degraded by mobility. Therefore, there a need for entities that act on behalf of users to simplify the tasks of discovering and managing network computing resources. It has been said that software agents are a solution in search of a problem. Mobile agents, however, are inherently distributed in nature, and therefore they represent a natural view of a distributed system. They provide an ideal mechanism for implementing complex systems, and they are well suited for applications that are communicationscentric such as Web-based network computing. Another attractive area of mobile agents is processing data over unreliable networks (such as wireless networks). In such an environment, the low reliability network can be used to transfer agents rather than a chunk. of data. The agent can travel to the nodes of the network, collect or process information without the risk of network disconnection, then return home. The publications of this doctorate by published works report on research undertaken in the area of distributed systems with emphasis on network computing paradigms, Web-based distributed computing, and the applications of mobile agents in Web-based distributed computing and wireless computing. The contributions of this collection of related papers can be summarized in four points. First, I have shown how to extend the Web to include computing resources; to illustrate the feasibility of my approach I have constructed a proof of concept implementation. Second, a mobile agent-based approach to Web-based distributed computing, that harness the power of the Web as a computing resource, has been proposed and a system has been prototyped. This, however, means that users will be able to use remote machines to execute their code, but this introduces a security risk. I need to make sure that malicious users cannot harm the remote system. For this, a security policy design pattern for mobile Java code has been developed. Third, a mediator-based approach to wireless client/server computing has been proposed and guidelines for implementing it have been published. This approach allows access to Internet services and distributed object systems from resource-constraint handheld wireless devices such as cellular telephones. Fourth and finally, a mobile agent-based approach to the Wireless Internet has been designed and implemented. In this approach, remote mobile agents can be accessed and used from wireless handheld devices. Handheld wireless devices will benefit greatly from this approach since it overcomes wireless network limitations such as low bandwidth and disconnection, and enhances the functionality of services by being able to operate without constant user input.