The steady state numerical solution and two dimensional hydrodynamic calculations of supergalactic winds generated by super star clusters are presented. Two possible regimes: quasi-adiabatic and strongly radiative are thoroughly discussed. It is shown that superwinds driven by compact and powerful starbursts undergo catastrophic cooling close to their sources, and establish a temperature distribution radically different from those obtained in the adiabatic solution. At the same time, both

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... ty and density radial distributions remain almost unchanged given the speed of the rapidly diverging flow. The rapid fall in temperature as a function of radius reduces the size of the zone radiating in X-rays and decreases the superwind X-ray luminosity. At the same time, cooling brings the 10^4 K boundary closer to the wind center, and promotes the establishment of an extended ionized fast moving envelope. This should show up as a weak and broad (∼ 1000 km s^-1) line emission component at the base of the much narrower line caused by the central HII region.