Four years of GOLF velocity time series have been used to study the low frequency part of the solar spectrum below 1.5 mHz. This paper discusses the methods already developed for the research of the low-degree low-order acoustic modes by Garcia et al. (2000) and for the gravity modes by Turck-Chieze et al. (2000). These methods are based on our knowledge of the general theoretical properties of the p and g modes that lead us to determine the statistical significance of the structures (multiplets) present in the GOLF spectrum in terms of p- and g-mode candidates. In addition to the search of single peaks, we try to detect multiplets (l = 1, 2 and 3) which allows us to lower the detection threshold while keeping the same confidence level. We will concentrate the discussion on the limits of this search that only takes into account those peaks above a selected statistical threshold giving an estimation of the possible uncertainties due to the solar noise and the nature of the solar resonances.