The results of studies of the higher electronic states of small halogenated molecules using resonance enhanced multiphoton ionisation (REMPI) spectroscopy are presented. A substantial part of this work concerned the Rydberg states of some methyl halides (methyl bromide, methyl iodide and methyl chloride). The assignment of these states was considerably added by polarisation studies. Also, the propensity rules apparent in the VUV and two-photon spectra of the diatomic halogens and interhalogens were found to be useful. Thus, features comprising the two-photon spectra of the methyl halides were assigned to Ω=0 and Ω=2 components of nd and np states. In the three-photon spectra, transitions to the above states were observed along with transitions to ns, np, nd and nf states, all with Ω=1. In fact, three-photon spectra are seen to be dominated by nf;1 series while nd series dominate the two-photon spectra. This study involves a considerable reappraisal of the identity of the states underlying Rydberg transitions in these methyl halides, apart from the first ns cluster. In a similar vein, Rydberg transitions in trifluoromethyl iodide were also investigated but their vibrational envelopes were found to depart from those seen for the methyl halides. This can be attributed to two causes: first, the increased amount of valence character of the orbital from which an electron is being promoted to a Rydberg orbital, as suggested by the appearance of the photoelectron spectrum, and second, the possibility of Rydberg-ion-pair interactions. This increased amount of valence character in the orbital from which an electron is promoted in a Rydberg transition also complicates the analysis of the two-photon spectrum of dichloromethane, especially in the energy region just below the first ionisation energy. Even so, the observed band systems are assginable to nd states of A₁ symmetry. Given that propensity rules in the spectra of the halogens are used to aid the spectral assignment of the above polyatomic molecules, an examination of the VUV spectroscopy of molecular chlorine in the 72000-77000 cm^-1 region, using (1+1') REMPI, is included as an example of the operation of these propensity rules.