Fluorescent nucleic acid base analogues (FBAs) are an important class of molecule used to study the structure and dynamics of DNA and RNA. These base analogues are molecules with structures that resemble one of the natural bases but which, unlike the natural bases, have high fluorescence quantum yields. 2-Aminopurine (2AP) has long been the most widely used fluorescent base analogue and is one of the few base analogues commercially available. One problem with 2AP is that it undergoes significant quenching when incorporated into DNA: the quantum yield decreases 100 fold from that of the free base, thus becoming too low for use in, for example, single molecule studies. A secondary problem is that the 305 nm absorption peak requires excitation in the UV. A variety of new fluorescent base analogues are being produced, with a view to remedying the deficiencies of 2AP and expanding the current range of use. The first part of this thesis explores the one-photon photophysical properties of several of these novel FBAs. The first of these novel FBAs is the 6-aza-uridine family. These compounds, analogues of uridine, have large Stokes shifts and their absorption and emission spectra are red-shifted in comparison to 2AP; their quantum yields as free bases have been shown to exceed that of 2AP and their environmental sensitivity has been demonstrated. Time-resolved measurements reported in this thesis indicate the presence of multiple emitting species. A density functional theory (DFT) study has been carried out to rationalise these emitting species as rotational isomers. Similar fluorescence lifetime measurements were made on a second class of FBAs, the quadracyclic adenine analogues, qANs; these results also indicated the presence of multiple emitting species. Experimental results show that these FBAs undergo excited-state proton transfer. The final FBA studied in this thesis is pentacyclic adenine, pA. This FBA showed some of the most promising characteristics of all the analogues investigated, such as a high quantum yield in both polar and non-polar solvents. A time-resolved investigation into pA-containing oligonucleotides indicated that in an oligonucleotide pA adopts multiple stacked conformations and its behaviour is highly sequence dependent. Several of these aforementioned fluorescent base analogues have absorption spectra in a region that makes them accessible to two-photon (2P) excitation with a Ti:Sapphire laser. In biological systems, multiphoton excitation has several advantages over one-photon excitation. By avoiding the use of ultraviolet light there is reduced phototoxicity. Out of focus photobleaching and autofluorescence are also minimised which leads to a higher signal-to-background ratio and allows deeper tissue penetration to be achieved. Fluorescent base analogues tend to have small Stokes shifts; this is another problem that can be overcome by using two-photon excitation. To be of potential use in multiphoton microscopy, a FBA must have a high two-photon absorption cross-section and a high two-photon brightness. Previously, the highest two- photon brightness measured for a fluorescent base analogue was less than 2 GM. Amongst the base analogues investigated here, are several that have higher two-photon brightness than ever reported for FBAs; these include pA which is shown to have the highest 2P brightness of a FBA in an oligonucleotide, 1.3 GM, and a member of the 6-azauridine family which as a free base has a 2P brightness of 18 GM. Detection of individual molecules represents the ultimate level of sensitivity and enables details about a molecular system that would otherwise be concealed using conventional ensemble techniques to be revealed. With the improved 2P brightness of the molecules measured in this thesis, it has become feasible to detect single FBA molecules using 2P excitation. To maximise the chance of detection, ultrafast, shaped laser pulses have been used as the excitation source. For the first time, the signal has been high enough and the molecule of interest sufficiently photostable such that 2P fluorescence correlation spectroscopy of a fluorescent base analogue in an oligonucleotide could be measured. In summary, this thesis reports the fluorescence lifetimes and two-photon cross-sections of a series of novel fluorescent base analogues, as well as fluorescence correlation spectroscopy measurements of the most promising candidates.