The vertical wind profiles measured by the SODAR and the radiosondes revealed that, under pure marine flow conditions (south-westerly flow), a Low-Level Jet (LLJ) was developed frequently between 150 and 300m height above the ground, that lasted for several hours. The corresponding vertical profiles of the potential temperature have shown that the MABL is characterized by very stable atmospheric conditions at the first 150-300 m (with mean potential temperature gradient 2oK/100m) followed by slightly stable to neutral conditions at higher levels. A more in depth analysis of the data for one experimental day (the 10th of August 2003) revealed the existence of an inertial oscillation of the wind vector, below and above the LLJ core. The Hilbert Huang transform (HHT), which is a thorough method to analyze non-stationary and nonlinear data, was applied to the SODAR measured v and u components in order to reveal the temporal characteristics of a non-stationary event, such as the inertial oscillations. The energyfrequencytime distribution (the Hilbert spectrum) was calculated at different levels, where large amplitudes at frequencies close to the inertial frequency (0.054 cycles/hour for Nantucket Island) were observed during certain time periods. These time periods correspond to those when the development of the LLJ was observed from both SODAR and radiosonde measurements. The estimated hodographs of the wind near the LLJ core, where the wind turned relative to the geostrophic wind with a period about seventeen hours, confirms the inertial oscillation of the wind vector. A possible mechanism for the development of the LLJ and the observed inertial oscillation of the wind vector is the frictional decoupling over the sea, due to the strong stability of the MABL lower layer. This plausible explanation is in agreement with the status of the marine flow and the calculated hodographs and Hilbert spectra, from the SODAR data, at different heights, which will be presented and discussed.