Abstract: BP neuraI networks were designed, thened and used t0 caregorize the data set andrecognize pattems in sunspot number vallation during the ascent and descent of solarcycles- A hist0rical data set of smo0thed monthly mean sunsPOt numbers for l75O ADtO the first half of l995 AD and the predicted values f0r the latter half of l995 tol996 were used. We 0btained good simulation results of the ascending Periods and smoothed monthly mean sunspot numbers for each ascent Period of Solar Cycle l-22and fairly good forecasting results of the ascending Period and the maximum ofsmoothed monthiy mean sunspot number for Solar Cycle 22- Flnally, the paper givesthe following eshmared values for Sol4f Cycle 23: The maximum of smoothedmonthly mean sunspot number is l96 and the ascending Period is 38 months-