Frequency-domain fluorescence lifetime imaging microscopy (FD-FLIM) is a fast and accurate way of measuring fluorescence lifetimes in widefield microscopy. However, the resolution of multiple exponential fluorescence decays has remained beyond the reach of most practical FD-FLIM systems. In this paper we describe the implementation of FD-FLIM using a 40 MHz pulse train derived from a supercontinuum source for excitation. The technique, which we term multi-harmonic FLIM (mhFLIM), makes it possible to accurately resolve biexponential decays of fluorophores without any a priori information. The system's performance is demonstrated using a mixture of spectrally similar dyes of known composition and also on a multiply-labeled biological sample. The results are compared to those obtained from time correlated single photon counting (TCSPC) microscopy and a good level of agreement is achieved. We also demonstrate the first practical application of an algorithm derived by G. Weber [1] for analysing mhFLIM data. Because it does not require nonlinear minimisation, it offers potential for realtime analysis during acquisition.