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Asymmetric driving behaviour in acceleration and deceleration processes under car-following (CF) state can affect traffic flow significantly. Thus, to improve the performance of CF models, the formation mechanism of the asymmetric driving characteristics (gap difference, reaction time difference, response intensity difference, discrete driving difference) and the internal relations between them should be investigated. Thus the quantification methods are proposed to study the asymmetry for each driving characteristic. Then the mean values of the gap, reaction time, discrete intensity, and response intensity at each velocity fragment in acceleration and deceleration process are measured respectively using the NGSIM data with the proposed quantification methods. By comparing these mean values in acceleration and in deceleration processes, the asymmetry of the gap, reaction time, discrete intensity and response intensity are validated. Moreover, the correlation analysis between the four asymmetric driving characteristics are implemented while the results indicate they influence each other, and the formation mechanisms of the four asymmetric driving behaviours are obtained.