Fifteen ROSAT PSPC observations available in the public archive are analysed in order to study time and spectral variability of the 12 Einstein Extended Medium Sensitivity Survey (EMSS) active galactic nuclei (AGN) detected by ROSAT with more than 2000 net counts. Time variability was investigated on 13 different timescales, ranging from 400 to 3.15 x 10(6) s (1 yr). Of the 12 sources analysed, only two do not show a significant variability on any time-scale. On a short time-scale, less than or equal to 20 per cent of AGN are seen as variable sources, while on a time-scale of greater than or equal to 100 000 s the fraction becomes greater than or equal to 50 per cent. However, one should bear in mind that the visibility function for variability is far from being uniform, and that small amplitude variations can be detected more often on a long time-scale than on a short timescale. Spectral variability was detected in only two sources: MS1158.6-0323 shows a hardening of the spectrum with increasing intensity, while MS2254.9-3712 shows a softening of the spectrum with increasing intensity. Finally, for one source (MS1416.3-1257), the observed variability is the result not of an intrinsic flux variation but, instead, of a variation in the column density along the line of sight. Since this variability has been observed on a time-scale of similar to 3.9 d, it is probably associated with the broad-line clouds.