The first parts of the thesis recalls the main features of the large MACRO experiment at the underground Gran Sasso Laboratory. It then describes the atmospheric muons measured by the experiment and the selection criteria to obtain and analyze a large sample of cosmic muons. The time series of MACRO muons was analyzed with two complementary approaches: search for the occurrence of bursts of muon events and search for periodicities in the muon time distribution. The Scan Statistics method was used in the first case and the Lomb-Scargle spectral analysis in the second case. The two techniques complete early analyses performed with folding methods. It is confirmed that the seasonal variation is the dominant periodic variation, and one also confirms the solar diurnal and sidereal modulations. A separate study concerns the analysis of the energy losses of the hypothetical Nuclearites in different materials and detectors; their importance for the searches performed by the MACRO and the SLIM experiments is discussed.
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