<p><strong>Abstract.</strong> In this paper, we have investigated geoeffectivity of near-Earth magnetic clouds during two periods concentrated around the last two solar minima. The studied magnetic clouds were categorised according to the behaviour of the Z-component of the interplanetary magnetic field (<i>B</i>_Z) into bipolar (<i>B</i>_Z changes sign) and unipolar (<i>B</i>_Z maintains its sign) clouds. The magnetic structure of bipolar clouds followed the solar cycle rule deduced from observations over three previous solar cycles, except during the early rising phase of cycle 24 when both <i>B</i>_Z polarities were identified almost with the same frequency. We found a clear difference in the number of unipolar clouds whose axial field points south (S-type) between our two study periods. In particular, it seems that the lack of S-type unipolar clouds contributed to relatively low geomagnetic activity in the early rising phase of cycle 24. We estimated the level of magnetospheric activity using a Dst prediction formula with the measured <i>B</i>_Z and by reversing the sign of <i>B</i>_Z. We found that bipolar clouds with fields rotating south-to-north (SN) and north-to-south (NS) were equally geoeffective, but their geoeffectiveness was clearly modified by the ambient solar wind structure. Geoeffectivity of NS-polarity clouds was enhanced when they were followed by a higher-speed solar wind, while the majority of geoeffective SN-polarity clouds lacked the trailing faster wind. A leading shock increased the geoeffectiveness of both NS- and SN-polarity clouds, in particular, in the case of an intense storm. We found that in 1995–1998, SN-polarity clouds were more geoeffective, while in 2006–2011 NS-polarity clouds produced more storms. A considerably larger fraction of events were trailed by a higher-speed solar wind during our latter study period, which presumably increased geoeffectivity of NS-polarity. Thus, our study demonstrates that during low and moderate solar activity, geoeffectivity of opposite polarity bipolar clouds may depend significantly on the surrounding solar wind structure. In addition, different polarities also give different temporal storm evolutions: a storm from an SN-polarity cloud is expected to occur, on average, half-a-day earlier than a storm from an NS-polarity cloud.</p>