  Observations at millimetre wavelengths are presented for a representative
sample of 22 X-ray-selected BL Lac objects (XBLs). This sample comprises 19
High-energy cutoff BL Lacs objects (HBLs), 1 Low-energy cutoff BL Lac object
(LBL) and 2 `intermediate' sources. Data for LBLs, which are mostly radio
selected BL Lac objects (RBLs) are taken from the literature. It is shown that
the radio--millimetre spectral indices ($\alpha_{5-230)$) of HBLs
($-0.29\pm0.15$) are slightly steeper than those of the LBLs ($-0.19\pm0.14$).
A correlation exists between $\alpha_{5-230}$ and 230 GHz luminosity. While
this correlation could be an artefact of comparing two populations of BL Lac
objects with intrinsically different radio properties it is also consistent
with the predictions of existing unified schemes which relate BL Lac objects to
Fanaroff- Riley class I radio galaxies. The HBLs have significantly flatter
submillimetre- X-ray spectral indices ($\alpha_{230-X}$) than the LBLs
($-0.68\pm0.07$ cf. $-1.08\pm0.06$)although the two intermediate sources also
have intermediate values of $\alpha_{230-X}\sim-0.9$. It is argued that this
difference cannot be explained entirely by the viewing angle hypothesis and
requires a difference in physical source parameters. The $\alpha_{230-X}$
values for the HBLs are close to the canonical value found for large samples of
radio sources and thus suggest that synchrotron radiation is the mechanism that
produces the X-ray emission. As suggested by Padovani & Giommi, the
inverse-Compton mechanism is likely to dominate in the LBLs requiring the
synchrotron spectra of these sources to steepen or cutoff at lower frequencies
than those of the HBLs.
