  We report on observations of the recently detected (Kuzmin et al. 2004) giant
pulses (GPs) from the pulsar PSR B0031-07 at 40 and 111 MHz. At 40 MHz the peak
flux density of the strongest pulse is 1100 Jy, which is 400 times as high as
the peak flux density of the average pulse (AP). Peak flux density of the GPs
compared to the AP peak flux density has roughly a power-law distribution with
a slope of -4.5. GPs at 40 MHz are essentially stronger than those ones at 111
MHz. This excess is approximately in inverse proportion to the frequency ratio.
The giant pulses are much narrower than the AP, and cluster in two narrow
regions of the AP near the peaks of the two components of the AP. Some of the
GPs emit at both phases and are double. The separation of the double GP
emission regions depends on frequency. Similarly to the frequency dependence of
the width of the AP, it is less at 111 MHz than at 40 MHz. This suggests that
GPs are emitted from the same region of the magnetosphere as the AP, that is in
a hollow cone over the polar cap instead of the light cylinder region. PSR
B0031-07 as well as the previously detected PSR B1112+50 are the first pulsars
with GPs that do not have a high magnetic field at the light cylinder. One may
suggest that there are two classes of GPs, one associated with high-energy
emission from outer gaps, the other associated with polar radio emission. The
GPs of PSR B0031-07 and PSR B1112+50 are of the second class. The dispersion
measure DM is found to be 10.900 +/- 0.003 pc/cm^{3}.
