The objective of this research is to investigate compression algorithms for the purposes o f medical archiving and remote diagnostics. A single X-ray of size 1024 by 1024 pixels at 8 bit resolution occupies approximately 1 Mbyte of storage space and takes approximately 8 minutes to transmit over a standard telephone line. There is a need to reduce both required storage space and transmission time. This is achieved by compressing the image. For archiving, a lossless compression algorithm is used and for remote diagnostics a lossy compression algorithm is used. The development of an application for the transmission of images from the server application to a client application using the Internet is also investigated. The performances of three lossless compression algorithms are investigated: Huffman Coding, Arithmetic Coding and Huffman Coding using Splay Trees. These algorithms are written in C, transformed into (Dynamic Linked Library) DLLs using Visual C++ for use in a Visual Basic application. The algorithms are tested on five images, three X-rays and two standard images, and compression ratio, compression time and decompression time are recorded for each. The lossy algorithm investigated is Transform Image coding using the Discrete Cosine Transform (DCT). This algorithm is written in C, transformed into a DLL using Visual C++ for use in a Visual Basic application. The algorithm is tested on five images, three X-rays and two standard images, and compression ratio, compression time, decompression time and mean square error for different quality factors are recorded for each image. The application is developed with a user-friendly Graphic User Interface (GUI) using Visual Basic. The client could choose an image from the server and then zo om in on any section of it. This can be used for remote diagnostics or as a reference tool. The application could also determine which DCT method to use to optimise the bandwidth, depending on the speed of the medium used.