We have gathered and analysed multicolour Geneva photometry and high-resolution spectroscopy of the stars HD121190 (B9V) and HD106419 (B9III) whose short-term periodic variability had become evident from their HIPPARCOS data. We find three significant frequencies for HD121190 in the Geneva data: 2.6831, 2.6199 and 2.4713 c d(-1) and classify the star as a slowly pulsating B star, the coolest single star of that class known to date. Its amplitude ratios are compatible with low-degree gravity modes. The spectra reveal low-amplitude variability and v sin i = 118 km s(-1) which implies that the star rotates at 26% of its critical velocity. For HD106419 we are unable to confirm the period found from the HIPPARCOS photometry in our ground-based data; rather we find a marginally significant frequency of 0.8986 c d(-1). This star is probably an evolved slowly pulsating B star with complex variations. HD106409 is also a moderate rotator as the spectra reveal v sin i = 78 km s(-1), which is also 26% of its critical velocity.