Using a special technique of data analysis, we have found 34 grand minima of solar activity in a 7700-year-long Δ14C record. The method used rests on a proper filtering of the Δ14C record and the extrapolation of verifiable results for the later history back in time. Additionally, we have applied a method of nonlinear dynamics, the recurrence rate, to back up the results. Our findings are not contradictory to the record of grand minima by Eddy [1977> but constitute a considerable extension. Hence it has become possible to look closer at the validity of models. This way, we have tested the model of Barnes et al. [1980>. There are hints for that the grand minima might solely be driven by the 209-year period found in the Δ14C record. ¿ American Geophysical Union 1996