The long-term hemispheric variation of the flare index is investigated. It is found that, (1) the phase difference of the flare index between the northern and southern hemispheres is about 6-7 months, which is near the time delay between flare activity and sunspot activity; (2) both the dominant and phase-leading hemisphere of the flare index is the northern hemisphere in the considered time interval, implying that the hemispheric asynchrony of solar activity has a close connection with the N-S asymmetry of solar activity.
Cross-correlation analysis and wavelet transform methods are proposed to investigate the phase relationship between the monthly sunspot group numbers in the solar northern and southern hemispheres.It is found that (1) the monthly sunspot group numbers in the northern hemisphere begin two months earlier than those in the southern one,which should lead to phase asynchrony between them but with a slight effect;(2) the Schwabe cycle length for the monthly sunspot group numbers in the two hemispheres obviously differs from each other,and the mean Schwabe cycle length of the monthly sunspot group numbers in the northern hemisphere is slightly larger than that in the southern one;(3) the monthly sunspot group numbers in the northern hemisphere precede those in the southern hemisphere during the years of about 1874-1927,after which,the southern hemisphere leads the northern hemisphere in the years 1928-1964,and then the northern hemisphere leads in time till the present.
