  We report a centimetre-wave (cm-wave, 5-31GHz) excess over free-free emission
in PNe. Accurate 31 and 250GHz measurements show that the 31GHz flux densities
in our sample are systematically higher than the level of optically thin
free-free continuum extrapolated from 250GHz. The 31GHz excess is observed,
within one standard deviation, in all 18 PNe with reliable 31 and 250GHz data,
and is significant in 9 PNe. The only exception is the peculiar object M2-9,
whose radio spectrum is that of an optically thick stellar wind. On average the
fraction of non-free-free emission represents 51% of the total flux density at
31GHz, with a scatter of 11%. The average 31-250GHz spectral index of our
sample is <alpha_{31}^{250}> = -0.43+-0.03 (in flux density, with a scatter of
0.14). The 31--250 GHz drop is reminiscent of the anomalous foreground observed
in the diffuse ISM by CMB anisotropy experiments. The 5--31 GHz spectral
indices are consistent with both flat spectra and spinning dust emissivities,
given the 10% calibration uncertainty of the comparison 5GHz data. But a
detailed study of the objects with the largest cm-excess, including the low
frequency data available in the literature, shows that present spinning dust
models cannot alone explain the cm-excess in PNe. Although we have no
definitive interpretation of our data, the least implausible explanation
involves a synchrotron component absorbed by a cold nebular screen. We give
flux densities for 37 objects at 31GHz, and for 26 objects at 250GHz.
