An exciting development in observational astronomy over the last 15 years has been the opening up of the submillimetre and millimetre atmospheric windows, to the extent that observations of external galaxies are now possible. This thesis presents the results of a millimetre/submillimetre-wave study of several nearby, infrared-bright, vigorously star-forming galaxies, in an attempt to investigate their molecular hydrogen content. In particular, it seeks to evaluate the relative merits of the two most commonly adopted molecular hydrogen ‘tracers’ - millimetre-wave transitions of the CO molecule and its isotopes, and submillimetre continuum emission from warm dust grains. Observational and theoretical evidence suggests that the effects of active star formation (in the form of intense UV fields, supernovae, etc.) on the CO emission may render it unreliable as a tracer of H2 in such galaxies. Dust continuum emission offers the potential for an independent probe of the interstellar molecular gas in starburst systems.The first part of the thesis concerns 450 /¿m mapping of the nearby starburst galaxy M82. In contrast to what might be expected if the CO and dust were both reliably tracing molecular hydrogen, the 450 gm map shows striking spatial dissimilarities to 12CO line maps of the same region. Consideration of isotopic CO data suggests that optical depth effects may in part explain the discrepancy, while the effect of the vigorous nuclear star formation on the excitation state of the CO may also be an important factor. The optically thin 450 gm continuum emission shows no strong evidence for dust temperature gradients across the galaxy and appears to trace reliably the distribution of the grains and hence the gas with which they are associated.As a follow-up to the M82 observations, 800 /¿m dust continuum maps were made of three more nearby star-forming galaxies, Maffei 2, M83 and IC342. Together with 450- 1100 /¿m photometry, these data fill an important gap in the long-wavelength spectra of such galaxies, enabling a study of the molecular material with which the dust is mixed. It is found that a single-temperature, modified blackbody dust spectrum cannot fit the observed submillimetre fluxes, unless the emissivity spectral index P = 1all the way to 1100//m, with corresponding dust temperatures ~45 K. While this scenario cannot be ruled out by current grain models, a multitemperature dust grain population seems more plausible for a composite object such as a galaxy. A two-temperature spectral fit suggests that ~90% of the dust may be cool (~20-25 K), somewhat surprising in a galaxy exhibiting observational evidence of vigorous nuclear star formation. Possible reasons for this, as well as the effect of a large cool-dust fraction on the derived gas column densities and masses, are discussed.In the final section of the thesis, 12C 0 and 13CO observations are presented of the infrared-bright, gas-rich galaxy Maffei 2. The CO emission from this galaxy is characterized by high main-beam brightness temperatures 2 K) and very wide lines (approaching 160 km s-1 FWHM at the centre). A simple rotating disc model shows that beam smearing of a steeply rising rotation curve fails to reproduce the observed linewidths, and that cloud velocity dispersions of ~100 km s“ 1 may be present in the central regions. Possible energy sources behind such large velocity dispersions are discussed. The 12CO and 13CO J = 2 -l and 1-0 antenna temperature ratios are compared point by point to investigate any large-scale variation of cloud excitation across the starburst region. It is found that a simplistic, single-temperature LTE analysis cannot reconcile the high observed 2- 1/1 -0 ratios with the low values of Tmb(12C O )/Tmb(13CO) that imply optically thick gas in the nuclear region. Non-LTE excitation effects in a multicomponent interstellar medium may conspire to make reliable interpretation of CO line data very difficult without detailed modelling
