This thesis covers the development of high-resolution model spectra of simple-stellar-populations (SSP) to be used in the measurement of the ages, metallicities and chemical abundances of unresolved extragalactic globular clusters (GCs). The models are compared to low- and high-resolution spectra of GCs in the Milky Way and M31 galaxies, whose properties are already known, to establish the effectiveness of both the SSP spectral grid and of the direct spectral fitting procedure employed in this work. The model SSP spectra were created using Dotter et al. (2007) isochrones, populated using the flux derived from a grid of stellar spectra, weighted by the Kroupa (2001) mass function. Models with varying mass loss from the red giant branch and varying numbers of He-burning stars were generated. The spectral grid currently covers a parameter range of 2 to 15 Gyrs in age, and -2.5 to 0 dex in [Fe/H] at an [alpha/Fe] of +0.4 dex. Metallicities derived for Milky Way GCs from Lick index comparisons to the model grid are in good agreement with values in the literature. The stellar spectral grid, from which the GC spectra are generated, has been created using ATLAS9 and SYNTHE. The spectra are at a resolution of R = 100,000 and cover a wavelength range from 3000 - 9000 Angstroms. Extensive work was undertaken in creating appropriate lists of atomic and molecular transition oscillator strength (log gf) values for this spectral grid. An automated program was created to alter the strengths of millions of atomic transition lines in the Kurucz atomic line lists to fit a model spectrum of appropriate parameters to that of the red-giant star Arcturus and to the Solar spectrum at shorter wavelengths (3000 - 3727 Angstroms). Comparisons to these observed spectra were made manually for several molecular lines and band-heads, and log gf values changed en-mass for all the lines of a given molecular species. The SSP spectra were compared to low-resolution spectra of Milky Way GCs. Integrated-light spectra of a large number of Galactic GCs were obtained from three sources: the Schiavon et al. (2005) Library of Integrated Spectra of Galactic Globular Clusters, taken using the Ritchey-Chretien spectrograph on the Blanco 4m telescope at Cerro Tololo Inter-American Observatory; spectra obtained through private communication with M. Bessell using the Double Beam Spectrograph on the 2.3m telescope at Siding Springs Observatory; and spectra obtained using the Robert Stobie Spectrograph on the 11m diameter Southern African Large Telescope. With resolutions of 1500 to 2800, abundances of individual elements could not be determined, but overall ages and metallicities were derived. The model spectra were fitted to the observed spectra using a Chi^2 minimisation procedure over large wavelength regions to fully utilise the information available in the spectra. Derived metallicity values were in agreement with literature values. However, age determinations were not consistent with those derived from photometric methods and had large associated uncertainties. The lack of age information in the spectra at such resolutions is a similar result to that found by other studies using the Schiavon data (eg. Mendel et al., 2007; Koleva et al., 2008). The SSP spectral grid was used to determine ages, metallicities and individual elemental abundances of three clusters (GCM06, GC5 and GC10) in the outer halo of M31. High-resolution spectra from Keck-HIRES were obtained through private communication with D. Forbes. Age and metallicity determinations were made simultaneously by fitting un-blended FeI lines and the H-beta and H-gamma lines. Diagnostic analysis (such as that done by Colucci et al., 2009) and simultaneous fitting of the FeI lines alone gave unrealistic age values that tended towards the lower limits (2 Gyrs) of the age grid. The age and metallicities derived in this work for these clusters are consistent with those found by Alves-Brito et al. (2009) using the same data. Abundances of a number of elements were derived from the high-resolution spectra. An overall enhancement of alpha-elements (from measurements of Ca, Si and Ti) was seen in all three clusters ([alpha/Fe] = 0.67 +/- 0.2, 0.63 +/- 0.2 and 0.5 +/- 0.2 dex for clusters GCM06, GC5 and GC10 respectively) which is greater than that found for other M31 GCs (Puzia et al., 2005; Colucci et al., 2009). A depletion in Mg compared to the other alpha-elements is seen, in accordance with patterns seen in both Milky Way and M31 GCs (Gratton et al., 2004; Colucci et al., 2009). All three clusters show varying levels of enhancements and depletion in the other measured elements (C, Sc, V, Cr, Mn, Ni, Ba), none of which follow the trends seen in Milky Way clusters. Comparisons to high-resolution spectra of Milky Way GCs, for which abundance ratios are known from the measurement of individual stars, need to be made to establish the accuracy of this elemental-abundance analysis. Overall, the system presented in this thesis is well designed to be used in the analysis of integrated-light spectra from distant, unresolved GCs. The uncertainties in the derived ages are still larger than desired, but the metallicity determination is very consistent when tested against clusters of known metallicities.