Aims. This study aims to improve our understanding of the occurrence and origin of grand solar maxima and minima. Methods. We first investigate the statistics of peaks and dips simultaneously occurring in the solar modulation potentials reconstructed using the Greenland Ice Core Project (GRIP) 10 Be and IntCal13 14 C records for the overlapping time period spanning between ∼1650 AD to 6600 BC. Based on the distribution of these events, we propose a method to identify grand minima and maxima periods. By using waiting time distribution analysis, we investigate the nature of grand minima and maxima periods identified based on the criteria as well as the variance and significance of the Hale cycle during these kinds of events throughout the Holocene epoch. Results. Analysis of grand minima and maxima events occurring simultaneously in the solar modulation potentials, reconstructed based on the 14 C and the 10 Be records, shows that the majority of events characterized by periods of moderate activity levels tend to last less than 50 years: grand maxima periods do not last longer than 100 years, while grand minima can persist slightly longer. The power and the variance of the 22-year Hale cycle increases during grand maxima and decreases during grand minima, compared to periods characterized by moderate activity levels. Conclusions. We present the first reconstruction of the occurrence of grand solar maxima and minima during the Holocene based on simultaneous changes in records of past solar variability derived from tree-ring 14 C and ice-core 10 Be, respectively. This robust determination of the occurrence of grand solar minima and maxima periods will enable systematic investigations of the influence of grand solar minima and maxima episodes on Earth's climate.