Analyzing the CME observations of SOHO/LASCO and SOHO/EIT, as well as solar wind observations of the WIND spacecraft, we identified the CME sources that led to the geomagnetic storms occurring from the late April to early May in 1998. Also we analyzed the solar-terrestrial events associated with intense geomagnetic storms in early May. The results show that the identification method of solar terrestrial events connected with geomagnetic storms we employed is feasible. In addition, we discussed the relationship between these geomagnetic storms and active regions, the east-west asymmetrical effect and the interactions between magnetic clouds and high-speed streams, etc.