Considering that a large amount of information, that transmitted in digital communication systems, accounts for graphic information, the development and improvement of methods and algorithms for compact representation of image data are very topical task.This paper shows the results of the study process of compact presentation of graphic information in computer systems, namely:− the basic methods of compact presentation of graphic information are considered. There are Gray reflex codes, progressive image compression, intuitive methods, JPEG, JPEG-LS, wavelet techniques, a mathematical transformation of the image;− the main indicators of algorithms for compact presentation of graphic information are considered. There are RLE, LZW, Huffman algorithm, JBIG, JPEG, Lossless JPEG, fractal algorithm, recursive algorithm, JPEG 2000;− advantages and disadvantages of methods and algorithms are revealed;− system analysis of opportunities for basic methods and algorithms for compression of graphical information is given.Investigated in the article impact of using combinations of methods of compact presentation of graphic information in computer systems at the results of the major compression algorithms will identify further ways to improve the degree of compression of graphic information.