A detailed study of two consecutive bright points observed simultaneously with the Coronal Diagnostic Spectrometer (CDS), the Extreme ultraviolet Imaging Telescope (EIT) and the Michelson Doppler Imager (MDI) onboard the Solar and Heliospheric Observatory (SOHO) is presented. The analysis of the evolution of the photospheric magnetic features and their coronal counterpart shows that there is a linear dependence between the EIT Fe XII 195 Å flux and the total magnetic flux of the photospheric bipolarity. The appearance of the coronal emission is associated with the emergence of new magnetic flux and the disappearance of coronal emission is associated with the cancellation of one of the polarities. In one of the cases the disappearance takes place ∼3-4 h before the full cancellation of the weakest polarity.The spectral data obtained with CDS show that one of the bright points experienced short time variations in the flux on a time scale of 420-650 s, correlated in the transition region lines (O V 629.73 Å and O III 599.60 Å) and also the He I 584.34 Å line. The coronal line (Mg IX 368.07 Å) undergoes changes as well, but on a longer scale. The wavelet analysis of the temporal series reveals that many of these events appear in a random fashion and sometimes after periods of quietness. However, we have found two cases of an oscillatory behaviour. A sub-section of the O V temporal series of the second bright point shows a damped oscillation of five cycles peaking in the wavelet spectrum at 546 s, but showing in the latter few cycles a lengthening of that period. The period compares well with that detected in the S VI 933.40 Å oscillations seen in another bright point observed with the Solar Ultraviolet Measurements of Emitted Radiation (SUMER) spectrometer, which has a period of 491 s. The derived electron density in the transition region was 3×1010 cm-3 with some small variability, while the coronal electron density was 5×108 cm-3.