To understand the magnetospheric substorm, it is necessary to determine whether its onset is externally triggered by the interplanetary magnetic field (IMF). We analyze the relationship between the IMF and the onset of classical substorms with well-defined onset times. A classical substorm is one that has auroral brightening and electrojet formation at onset, followed by poleward expansion of the region of bright aurora. Substorms meeting these criteria are identified using Canadian Auroral Network for the OPEN Program United Study ground photometer data. We find that a clear IMF trigger (a northward turning or a reduction in the magnitude of the y component) can be identified for 14 of the 20 substorms used in our study. All but one of the identified triggers are northward turnings. We develop a rigorous set of criteria that represents these triggers. By applying the criteria to a large set of IMF data, we find that it is essentially impossible for the observed association between triggers and substorms to happen by chance. This demonstrates that substorm triggering is a real phenomenon and not the result of the requirement that the IMF be southward before but not after a substorm. We also find that spatial structure in the plane perpendicular to the Earth-Sun line critically affects whether or not a trigger is observed from a particular IMF monitor; the probability of seeing a trigger for the substorms in our study is 89% for monitors that are <30 RE from the Earth-Sun line but only 50% for monitors 30 RE to 56.7 RE from the Earth-Sun line. Thus a well-defined IMF trigger is associated with most of substorms considered here, and the probability of trigger identification is a strong function of IMF monitor distance from the Earth-Sun line. Given this limitation of trigger identification due to spatial structure, our observations imply that a large majority of classical substorms are triggered by the IMF. We also obtain estimates of ~9 min for the mean time delay between magnetopause contact of an IMF trigger and substorm onset and ~64--72 min for the median growth-phase period of southward IMF that precedes triggered classical substorms. ¿ 1997 American Geophysical Union