The relationship between the geomagnetic aa index and the winter North Atlantic Oscillation (NAO) has previously been found to be nonstationary, being weakly negative during the early 20th century and significantly positive since the 1970s. The study reported here applies a statistical method called the generalized additive modeling (GAM) to elucidate the underlying physical reasons. We find that the relationship between aa index and the NAO during the Northern Hemispheric winter is generally nonlinear and can be described by a concave shape with a negative relation for small to medium aa and a positive relation for medium to large aa. The nonstationary character of the aa-NAO relationship may be ascribed to two factors. First, it is modulated by the multidecadal variation of solar activity. This solar modulation is indicated by significant change points of the trends of solar indices around the beginning of solar cycle 14, 20, and 22 (i.e., ∼1902/1903, ∼1962/1963, and ∼1995/1996). Coherent changes of the trend in the winter time NAO followed the solar trend changes a few years later. Second, the aa-NAO relationship is dominated by the aa data from the declining phase of even-numbered solar cycles, implying that the 27 day recurrent solar wind streams may be responsible for the observed aa-NAO relationship. It is possible that an increase of long-duration recurrent solar wind streams from high-latitude coronal holes during solar cycles 20 and 22 may partially account for the significant positive aa-NAO relationship during the last 30 years of the 20th century.