The theoretical sensitivity of Love wave and layer-guided shear horizontal acoustic plate mode (SH-APM) sensors for viscoelastic guiding layers and general loading by viscoelastic materials is developed. A dispersion equation previously derived for a system of three rigidly coupled elastic mass layers is modified so that the second and third layers can be viscoelastic. The inclusion of viscoelasticity into the second, wave guiding layer, introduces a damping term, in addition to a phase velocity shift, into the response of the acoustic wave system. Both the waveguiding layer and the third, perturbing layer, are modeled using a Maxwell model of viscoelasticity. The model therefore includes the limits of loading of both nonguided shear horizontal surface acoustic wave and acoustic plate mode (APM) sensors, in addition to Love wave and layer-guided SH-APM sensors, by rigidly coupled elastic mass and by Newtonian liquids. The three-layer model is extended to include a viscoelastic fourth layer of arbitrary thickness and so enable mass deposition onto an immersed Love wave or layer-guided SH-APM sensor to be described. A relationship between the change in the complex velocity and the slope of the complex dispersion curve is derived and the similarity to the mass and liquid sensor response of quartz crystal microbalances is discussed. Numerical calculations are presented for the case of a Love wave device in vacuum with a viscoelastic waveguiding layer. It is shown that, while a particular polymer relaxation time may be chosen such that the effect of viscoelasticity on the real part of the phase speed is relatively small, it may nonetheless induce a large insertion loss. The potential or the use of insertion loss as a sensor parameter is discussed.