The paper presents selected results of experimental research on motor truck tyres in transient sideslip conditions. The tests were carried out with the use of two test facilities: a quasi-static test stand and a trailer for dynamic tyre testing. Results of measurements of the lateral reaction transmitted by the tyre of a vehicle wheel have been presented here against the background of changes in the wheel motion conditions. During the tests, quick changes were forced in the tyre slip angle, with single pulse, stepwise, and oscillating inputs being applied. A method of observing and analysing the share of tyre relaxation in the process of transmission of the lateral reaction in transient tyre sideslip conditions has been presented. The measurement results obtained contribute to elucidation of the tyre relaxation issues. Simultaneously, they constitute a source of data that make it possible to verify a model of tyre-road interaction where tyre relaxation would be taken into account.