In this work preliminary results on the study of the structural characteristics of the turbulent Marine Atmospheric Boundary Layer (MABL) are presented. Measurements used here were conducted in the framework of The Coupled Boundary Layers Air-Sea Transfer Experiment in Low Wind (CBLAST-Low) project. A number of in situ (fast and slow sensors) and remote sensing (SODAR) instruments were deployed on the coast of Nantucket Island, MA, USA. The measurements of the mean wind, variances of the three components of the wind, the stability and momentum fluxes from the acoustic radar (SODAR) revealed the variation of the depth, turbulence characteristics, and stability of the MABL in response to the background flow. More specifically, under light south-southwesterly winds, the wind direction for MABL study, the atmosphere was very stable and low values of turbulence were observed. Under moderate to strong southwesterly flow, less stable and neutral atmospheric conditions appeared and the corresponding turbulent quantities were characterized by higher values. The SODAR measurements, with high temporal and spatial resolution, also indicated large magnitude of momentum fluxes at higher levels, presumably associated with the shear forcing near the developed low-level jet. The measurements from the in-situ instrumentation confirmed that the MABL typically has negative momentum and sensible heat fluxes consistent with stable stratification while strong diurnal variations were typical for the land surface atmospheric boundary layer (ABL). The estimated surface momentum flux confirmed its dependence on the wind speed and the stability factor (z/L). The developed internal ABL at the experimental site was in general less than 10m during the night and can reach 15m heights during the day, particularly under low-wind conditions.