A theory of the strip coupled acoustic surface wave amplifier, the acoustic surface wave strip coupler, and the strip coupled acoustic surface wave parametric device is given. This theory makes use of a space harmonic expansion and variational techniques to determine the impedance looking into an individual strip. The resulting model accurately predicts the experimental results obtained with strip couplers and indicates that for optimum coupling the ratio of strip width to gap spacing should be unity. Strips can be used to couple from the piezoelectric medium to a semiconductor to make amplifiers and nonlinear signal processing devices. When used in amplifiers, strip coupling should reduce the power dissipation for a given gain by orders of magnitude and greatly increase the gain at low frequencies. In parametric devices, the strips eliminate the need for microscopic air gaps and should increase the processing efficiency by orders of magnitude.