Using annual average values, the relationships are examined of the geomagnetic indices SYM-H, ASY-H, and Dst with solar wind parameters in 1981–2015. The data used was divided into two samples according to the sign of the north-south component Bn of the interplanetary magnetic field (IMF). Variations in the annual average values of each of the Dst, SYM-H, and ASY-H indices for southward and northward IMF have been found to be similar and their linear correlation coefficients r to be high: 0.871, 0.863, and 0.943 respectively. The similarity between variations of the indices with different signs of Bn is probably due to their connection with the number of sunspots. It has been established that Dst, SYM-H, and ASY-H depend on the solar wind parameter β: their absolute values decrease with increasing β, regardless of Bn sign. The decrease in the indices with increasing β is likely to be caused by the transition of the magnetosphere to a quiet state due to the increasing predominance of thermal pressure over magnetic one in the solar wind and a decrease in the level of solar wind turbulence. SYM-H and ASY-H have been found to reveal the closest relationships with β, whereas SYM-H more strongly depends on β for southward IMF (r=0.744) than for northward IMF (r=0.677). On the contrary, for ASY-H r=–0.741 at northward IMF and r=–0.719 at southward IMF. Similar to SYM-H, Dst (to a lesser extent) significantly correlates with β at southward IMF (r=0.629) and weaker at northward IMF (r=0.456).