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 1 100 Jy , which is 400 times as high as the peak flux density of the average pulse ( AP ) . A pulse whose observed peak flux exceeded the peak of the AP by more than a factor of 200 is encountered approximately once in 800 observed periods . Peak flux density of the GPs compared to the AP peak flux density S ^ { GP } _ { peak } / S ^ { AP } _ { peak } 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 ~ { } \pm~ { } 0.003 ~ { } \mathrm { pc~ { } cm ^ { -3 } } .