Positron emission tomography (PET) imaging is a versatile modality with the ability to examine metabolic factors in individual tissues in vivo. It is an indispensable tool for research and treatment planning of diseases such as cancer. However, versatility could be increased if it were possible to image multiple tracers simultaneously. Such an ability could be important in developing a treatment strategy for diseases that remain intractable in the majority of cases, such as advanced glioma.Metabolic imaging with PET using target specific radiotracers has been shown to improve the delineation of tumour margins and provide increased information about tumour microbiology. However, the physical properties of radiotracers limits their combined use, such that imaging of more than one molecular target using PET is not generally considered feasible.Multiplexing PET imaging (dual-tracer PET) offers a solution that allows for individual PET imaging of two or more individual radiotracers, within the same scanning session. Although the technique was first proposed in the 1980s, this approach is not utilised despite offering significant advantages such as multiple target imaging and validation of new PET radiopharmaceuticals. Reasons for this lack of implementation may include assumptions about the potential loss in image quality and the logistics in synthesizing multiple PET tracers simultaneously.In this PhD, Dual-Tracer PET imaging techniques were developed, with a focus on the ability to validate chosen dual-tracer protocols prior to scanning. A set of techniques was devised to handle cases of increasing complexity: (initially) where the first tracer can be assumed to be static after a certain amount of time; secondly where the first tracer has a constant slow uptake that can be assumed to be linear; and the general case where the first tracer retains residual dynamics, with the use of a basis pursuit to separate the signals.These approaches were tested by applying them to specific, clinically relevant use cases.Development of these techniques has provided a framework for study designers to effectively implement dual-tracer PET imaging with confidence for the validation of new tracers, the investigation of cases where multiple biological factors are important and the further development of diagnosis and treatment in future applications. Finally, by utilising iii basis pursuit approaches, it is possible to consider any combination of tracers regardless of tracer and without devising specific model of uptake within tissue.iv