Although self-assembled monolayers (SAMs) are promising candidates for interfacial lubricants in micro-electromechanical systems, the relationship between the monolayer structure and its viscoelastic properties is not understood. Using Acoustic Wave Damping (AWD), we have measured the complex shear modulus of linear alkane thiol monolayers, HS(CH2)n-1 CH3 denoted as Cn, on Au(111)-textured substrates. The AWD technique measures the elastic energy storage and dissipative loss within a SAM adsorbed onto the electrodes of a quartz crystal microbalance. For C12, C14, and C18, SAMs, the storage modulus increases with alkane chain length, but the loss modulus exhibits no systematic correlation. To investigate the origins of energy dissipation, we used a new, high-sensitivity oscillator circuit to simultaneously monitor the adsorption kinetics and acoustic damping during monolayer growth from the gas phase. For both C9 and C12 thiols, the dissipation in the growing monolayer can be correlated with distinct two-dimensional fluid phases and the nucleation and growth of condensed-phase islands.