High gradient acceleration is a core challenge of accelerator physics. Achieving high gradients is made challenging by issues relating to rf breakdown and pulsed surface heating, which are caused by intense surface fields in the accelerating cavities. The excitation of multiple harmonically related modes within a cavity could reduce the onset of these effects. The temperature rise from pulsed surface heating can be reduced by lowering the average magnetic surface field squared and rf breakdown could be avoided by creating an asymmetry between the anode and cathode surface electric fields. This thesis will present several different cavity designs that show a reduction in the temperature rise on the surface of over 10% for second and third harmonic cavity structures or an asymmetry in the surface electric anode and cathode fields of a factor of 2. The harmonic mode could have undesirable consequences for beam stability. A study of the longitudinal beam dynamics is included that will derive the equations governing the longitudinal motion and show that the harmonic mode will have a minor and predictable effect on the rf bucket. The Compact LInear Collider (CLIC) is a major contender for the next generation of lepton linear colliders and is made challenging by high power requirements and distribution throughout the linac. A high current drive beam is decelerated parallel to the main linac in order to create the required rf power, which can overcome some of these issues. This thesis will describe a novel design for a CLIC-like accelerating structure, using collinear acceleration through fundamental mode detuned cavities. The design will accommodate interleaved drive and test bunches, such that the drive bunches are decelerated and the test bunches are accelerated within the confines of the same cavity which can result in high transformer ratios. The analytical theory based on the circuit model will be verified by time domain simulations. A multi-harmonic detuned accelerating structure is introduced that exhibits the properties of pulsed surface heating reduction and can be used for collinear acceleration. Time domain simulations will verify the transformer ratio to within 3% of theoretical predictions and the average magnetic field squared reduction will be within 20% of the value calculated from eigenmode simulations.