The Global Positioning System (GPS) provides an alternative way to investigate ionospheric irregularities and their effects on the radio wave propagation. The method is based on fluctuations of the total electron content (TEC) resulted from the ionospheric plasma irregularities. Previous studies have showed the correlation between the radiowave intensity (including GPS signals) and ionospheric irregularities during magnetic storm periods. In this study, phase fluctuations derived from GPS signals are used to address aspects of the ionospheric storm events during the low irregularity activity months. We analyze data from seven GPS stations located in Central-and South-America during eight magnetic storms occurred from 1997 to 2000. It is found that, in general no significant feature in the phase fluctuation is observed during the low irregularity activity months, except during the 26 August 1998 and the 15 July 2000 storms. A detailed study shows that the GPS phase fluctuations develop when the Dst index begins to decrease significantly. This phenomenon cannot be compared directly to previous observations and model results due to the fundamental difference in the background levels of irregularity activity. To better understand the generation of ionospheric irregularities during the storm period of the low irregularity activity months, the temporal relationship between the magnetic Dst index, equatorial anomaly TEC, and the GPS phase fluctuations are examined and discussed.