Starburst-driven superwinds in galaxies have the potential to transport interstellar material (ISM) to the intergalactic medium (IGM). The mechanism is expected to be a function of the gravitational potential of the host galaxy, low-mass galaxies being more likely to lose mass in an outflow. In order to investigate the possibility of dwarf galaxies shedding enriched, hot material into the IGM, we selected, in addition to data directly obtained by us, archival data on a sample of nearby dwarf starburst galaxies that were observed with the Chandra X-Ray Observatory (employing the ACIS-S3 CCD). The sample comprises eight objects: I Zw 18, VII Zw 403, IC 2574 (actually a nonstarburst galaxy but containing a bright starburst region), NGC 1569, NGC 3077, NGC 4449, NGC 5253, and He 2-10. Toward each of the targets we detected unresolved X-ray sources (at the 1 .1 resolution of Chandra), which are thought to be related to the galaxies. They are in general located in the vicinity of bright H ii regions or on the rims of supergiant shells. This, plus their spectral properties, points at high-mass stars being ultimately responsible. Diffuse X-ray emission, attributed to the emission from a hot thermal plasma, was detected in NGC 1569, NGC 3077, NGC 4449, NGC 5253, and He 2-10. The size of the diffuse component varies between 1 and 10 kpc. Averaged over the entire galaxy, we derive X-ray luminosities of the hot gas in the range of 10–10 ergs s , temperatures of ∼ K, 1 6 3 # 10 and densities of ∼0.02 cm (MeKaL models; is the 0.5 3 f f v v volume filling factor). The pressures were found to be P/k ≈ K cm . This is an order of magnitude higher than 5 0.5 3 10 fv typical pressures of the ISM in the Milky Way, hence the hot gas must be expanding. The values quoted critically depend on the plasma models used for the fits; a disconcerting result is that equally good “best” fits can be obtained that vary by up to an order of magnitude in their unabsorbed X-ray luminosities. One of the galaxies, NGC 3077, is studied in depth in this thesis. In this galaxy, the hot gas is found to be confined to expanding Ha superbubbles. As in the other galaxies with extended emission, the energy provided by the starburst is high enough, in principle, for the hot gas to escape from the gravitational potential of the respective host. However, additional work is needed to overcome an extended gaseous environment. We argue that in NGC 3077, at least some of the gas is lost toward the north but not toward the south. The situation is similar in NGC 4449, where the hot gas extends beyond the optical disk but seems to be confined by a large H i ring of tidal origin. In NGC 1569 and NGC 5253, the X-ray emission resembles a freely flowing wind. This picture is supported by steeper volume density profiles of the hot gas as compared to NGC 3077 and NGC 4449. Normalized, azimuthally averaged surface brightness profiles of the Ha and the diffuse X-ray emission are very similar, suggesting a common origin. A comparison of the hot-gas masses derived on the basis of the X-ray data with estimates of stellar mass loss reveals that, except for NGC 3077, additional material (of up to a factor of 100) must have become entrained in the expanding X-ray plasma (mass loading). If diffuse, hot gas exists in I Zw 18, VII Zw 403, or IC 2574 with similar properties as that in the other objects, the low metallicity of these galaxies can explain the fact that they remained below the detection threshold. However, alternative explanations such as larger than predicted internal absorption, substantially lower or higher temperatures of the plasma, or loss of the coronal gas through blowout cannot be excluded at present.