The experimental configuration and the computational algorithms for performing multiple frequency fluorescence lifetime imaging microscopy (mfFLIM) are described. The mfFLIM experimental set-up enables the simultaneous homodyne detection of fluorescence emission modulated at a set of harmonic frequencies. This was achieved in practice by using monochromatic laser light as an excitation source modulated at a harmonic set of frequencies. A minimum of four frequencies were obtained by the use of two standing wave acousto-optic modulators placed in series. Homodyne detection at each of these frequencies was performed simultaneously by mixing with matching harmonics present in the gain characteristics of a microchannel plate (MCP) image intensifier. These harmonics arise as a natural consequence of applying a high frequency sinusoidal voltage to the photocathode of the device, which switches the flow of photoelectrons 'on' and 'off' as the sinus voltage swings from negative to positive. By changing the bias of the sinus it was possible to control the duration of the 'on' state of the intensifier relative to its 'off' state, enabling the amplitude of the higher harmonic content in the gain to be controlled. Relative modulation depths of 400% are theoretically possible from this form of square-pulse modulation. A phase-dependent integrated image is formed by the sum of the mixed frequencies on the phosphor of the MCP. Sampling this signal over a full period of the fundamental harmonic enables each harmonic to be resolved, provided that the Nyquist sampling criterion is satisfied for the highest harmonic component in the signal. At each frequency both the phase and modulation parameters can be estimated from a Fourier analysis of the data. These parameters enable the fractional populations and fluorescence lifetimes of individual components of a complex fluorescence decay to be resolved on a pixel-by-pixel basis using a non-linear fit to the dispersion relationships. The fitting algorithms were tested on a simulated data set and were successful in disentangling two populations having 1 ns and 4 ns fluorescence lifetimes. Spatial invariance of the lifetimes was exploited to improve the accuracy significantly. Multiple frequency fluorescence lifetime imaging microscopy was then successfully applied to resolve the fluorescence lifetimes and fluorescence intensity contributions in a rhodamine dye mixture in solution, and green fluorescent protein variants co-expressed in live cells.