Compression is useful to reduce the number of bits needed to represent to data. Compressing saves speed file transfer, and decrease costs for storage hardware and network bandwidth. Compression is applied by a program that uses a algorithm to determine how to shrink the size of data. There are number of data compression techniques used and they can be categorized as Lossy and Lossless Compression methods. This paper examines Huffman and arithmetic lossless data compression algorithms and compares their performance. A set of selected algorithms are implemented to examine the performance in compressing text data. An experimental comparison of a number of two lossless data compression algorithms i.e. arithmetic and Huffman is implemented in this paper. In this paper, some of the Lossless data compression methods and their performance are given.