The construction of two femtosecond dye lasers, a colliding pulse modelocked laser and a synchronously pumped laser is described. The amplification of these lasers in a four stage Nd:YAG pumped system, which operates at 10 Hz and in a copper vapour pumped, bow-tie amplifier operating at 6.5 kHz, is also described. These lasers are both used for transient absorption experiments and replace out-dated picosecond apparatus. Consequently, the thesis discusses the differences between the picosecond and femtosecond time domains from a practical point of view. The technique of transient absorption is described, paying particular attention to the technical difficulties associated with the use of femtosecond pulses. Flexible data collection devices, which control the experiments at both 10 Hz and 6.5 kHz, have been built. The interfacing of these units to an Apple Macintosh computer, via two National Instruments extension cards on a shared bus, is covered in detail. A novel technique for the measurement of transient absorption kinetics in a single laser pulse has been developed, which is discussed critically. The dyes, thionine and methylene blue are known to bind statically to DNA. The close proximity of the dyes to the nucleotides allows the singlet states to be quenched by electron transfer from the nucleotide segments. The kinetics of the electron transfer from adenine and guanine sites is reported. The fastest reaction occurs in under 1 ps. The ultrafast excited state properties of polyactetylene and a novel block copolymer of norbornylene and polyacetylene, prepared by the Durham route, are investigated. The dynamics of the polyacetylene excited states are reproduced in the copolymer, which has been shown to be useful in non-linear optical devices.