The sliding friction between two highly oriented monolayers has been studied by using molecularly smooth mica substrates in the form of contacting orthogonal cylinders. The monolayers in the form of various normal alipathic carboxylic acids and their soaps were deposited with the aid of the Langmuir-Blodgett technique by transfer from aqueous substrates. The normal alkyl group has been varied in length from 14 to 22 methylene repeat units. Data are reported also on the influence of partial saponification of the carboxylic acid and fluorination of the alkyl chain. Most of the investigation has been confined to two contacting single monolayers although a limited amount of data is presented for multilayers sliding over one another. The character of the sliding motion depends not only on the machine but also on the monolayers, particularly their chemistry. Most of the monolayers studied provide a continuous rate of energy dissipation. However, a small number, such as certain soaps, show discontinuous or stick-slip motion. The experimental arrangement allows simultaneous measurement of the sliding frictional force, contact area and film thickness to be made during sliding. In some experiments this friction is the monotonic sliding friction but in others it is the mean maximum value during the stick phase. The film thickness measurement is accurate to 0.2 mm which allows a precise assessment of the shear plane during sliding. In all cases the monolayers and multilayers were found to be extremely durable and shear invariably occurred at the original interface between the monolayers. The sliding friction data are presented as the dynamic specific friction force or interface shear strength, and a number of contact variables have been examined. These include the applied normal load per unit contact area or mean contact pressure, the temperature and the sliding velocity. The interface shear strength is found, to a good approximation, to increase linearly with mean contact pressure but to decrease linearly with temperature in the ranges studied. The influence of sliding velocity is more complex. In the case where intermittent motion is detected the mean maximum values decrease linearly with the logarithm of the velocity.