Method for serial data transmission between a position measuring system (20; 200; 2000) and a processing unit (10; 100; 1000), in which the position measuring system (20; 200; 2000) transmits position data (POS_DAT, POS_DAT') and further data (DAT, DAT') in serial form as digital data words to the processing unit (10; 100; 1000), - wherein the data to be transmitted are split into time-critical and time-uncritical data and the position data (POS_DAT, POS_DAT') and also position request commands (POS_RQ, POS_RQ') are time-critical data, whereas further data (DAT, DAT') in the form of supplementary data (ADD_DAT, ADD_DAT') and supplementary data commands (DAT_RQ, DAT_RQ') are time-uncritical data, and - wherein a position request command (POS_RQ, POS_RQ') from the processing unit (10; 100; 1000) prompts current position data (POS_DAT, POS_DAT') to be transmitted from the position measuring system (10; 100; 1000) to the processing unit (20; 200; 2000) and, following the position data (POS_DAT, POS_DAT'), further data (DAT, DAT') to be transmitted from the position measuring system (20; 200; 2000) to the processing unit (10; 100; 1000), the processing of said further data being time-uncritical, and - wherein, in the event of a position request command (POS_RQ) arriving in the position measuring system (20; 200; 2000) during the transmission of time-uncritical data (DAT, DAT') to the processing unit (10; 100; 10000), the transmission of the time-uncritical data (DAT, DAT') is terminated and instead the requested current position data (POS_DAT) are transmitted to the processing unit (10; 100; 1000), and - wherein a plurality of different position request commands (POS_RQ") exist that have different associated execution priorities and that, in the event of transmission to the position measuring system (20; 20000; 2000), prompt transmission of the current position data (POS_DAT) to the processing unit (10; 100; 1000) in accordance with their associated execution priorities. - wherein the data to be transmitted are split into time-critical and time-uncritical data and the position data (POS_DAT, POS_DAT') and also position request commands (POS_RQ, POS_RQ') are time-critical data, whereas further data (DAT, DAT') in the form of supplementary data (ADD_DAT, ADD_DAT') and supplementary data commands (DAT_RQ, DAT_RQ') are time-uncritical data, and - wherein a position request command (POS_RQ, POS_RQ') from the processing unit (10; 100; 1000) prompts current position data (POS_DAT, POS_DAT') to be transmitted from the position measuring system (10; 100; 1000) to the processing unit (20; 200; 2000) and, following the position data (POS_DAT, POS_DAT'), further data (DAT, DAT') to be transmitted from the position measuring system (20; 200; 2000) to the processing unit (10; 100; 1000), the processing of said further data being time-uncritical, and - wherein, in the event of a position request command (POS_RQ) arriving in the position measuring system (20; 200; 2000) during the transmission of time-uncritical data (DAT, DAT') to the processing unit (10; 100; 10000), the transmission of the time-uncritical data (DAT, DAT') is terminated and instead the requested current position data (POS_DAT) are transmitted to the processing unit (10; 100; 1000), and - wherein a plurality of different position request commands (POS_RQ") exist that have different associated execution priorities and that, in the event of transmission to the position measuring system (20; 20000; 2000), prompt transmission of the current position data (POS_DAT) to the processing unit (10; 100; 1000) in accordance with their associated execution priorities.