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We present the results of recent $BeppoSAX$ observations of the two BL Lac objects OJ 287 and MS 1458+22 in bright optical states and of simultaneous photometric measurements in the bandpasses from $I$ to $U$. OJ 287 was observed in November 2001 and MS 1458+22 in February of the same year. The X-ray flux of OJ 287 was rather low, $F$(2-10 keV$) = (1.35\pm0.15)\times 10^{-12}$ erg cm$^{-2}$ s$^{-1}$ and its spectrum is well described by a single power law with an energy index $0.45\pm0.08$, flatter than that measured in the optical, equal to $1.53\pm0.03$. The X-ray emission of MS 1458+22 was characterized by a low flux level of $F$(2-10 keV$) = (7.5\pm0.6)\times 10^{-13}$ erg cm$^{-2}$ s$^{-1}$, with a steeper spectral index of $1.71\pm0.15$, while in the optical it was $0.99\pm0.06$. We show that the broad-band SEDs of these two sources can be well represented by log-parabolic spectral laws and evaluate their parameters. This law, already observed for the synchrotron components of other BL Lac sources, can be explained if the emitting particles are accelerated by some statistical mechanism having a probability of energy gain that is a decreasing function of the energy itself.

Eight optical and four radio observatories have been intensively monitoring the BL Lac object 0716+714 in the last years: 4854 data points have been collected in the $UBVRI$ bands since 1994, while radio light curves extend back to 1978. Many of these data, which all together constitute the widest optical and radio database available on this object, are presented here for the first time. Four major optical outbursts were observed at the beginning of 1995, in late 1997, at the end of 2000, and in fall 2001. In particular, an exceptional brightening of 2.3 mag in 9 days was detected in the $R$ band just before the BeppoSAX pointing of October 30, 2000. A big radio outburst lasted from early 1998 to the end of 1999. The long-term trend shown by the optical light curves seems to vary with a characteristic time scale of about 3.3 years, while a longer period of 5.5–6 years seems to characterize the radio long-term variations. In general, optical colour indices are only weakly correlated with brightness; a clear spectral steepening trend was observed during at least one long-lasting dimming phase. Moreover, the optical spectrum became steeper after $\rm JD \sim 2\,451\,000$, the change occurring in the decaying phase of the late-1997 outburst. The radio flux behaviour at different frequencies is similar, but the flux variation amplitude decreases with increasing wavelength. The radio spectral index varies with brightness (harder when brighter), but the radio fluxes seem to be the sum of two different-spectrum contributions: a steady base level and a harder-spectrum variable component. Once the base level is removed, the radio variations appear as essentially achromatic, similarly to the optical behaviour. Flux variations at the higher radio frequencies lead the lower-frequency ones with week–month time scales. The behaviour of the optical and radio light curves is quite different, the broad radio outbursts not corresponding in time to the faster optical ones and the cross-correlation analysis indicating only weak correlation with long time lags. However, minor radio flux enhancements simultaneous with the major optical flares can be recognized, which may imply that the mechanism producing the strong flux increases in the optical band also marginally affects the radio one. On the contrary, the process responsible for the big radio outbursts does not seem to affect the optical emission.