This Thesis is concerned with the physical nature of the outer atmospheres of the 'hybrid' bright giants. These stars show C IV emission and evidence of cool, fast winds - unlike giants of similar effective temperature, which possess only cool chromospheres. The K3 II star ι Aur is studied in detail. Chapter 1 discusses the importance of these stars in the context of the HR diagram. Chapter 2 examines the evolutionary status of the 'hybrid' bright giants and sets out the physical parameters which are adopted in the atmospheric modelling. In Chapter 3, the high and low resolution IUE data extracted for ι Aur are discussed. In Chapter 4, the emission line fluxes and profiles are analysed and an emission measure distribution is calculated. Simple hydrostatic models of the transition region and corona are constructed. Chapter 5 describes the methodology employed to construct model chromospheres using non-LTE radiative transfer. In Chapter 6, computations of the chromospheric structure of a 'hybrid' star are presented for the first time. Calculations made for the first time show that the excitation of the Fe I y⁵G^o₃ level by the Mg II k line can produce the observed emission in other transitions from the J = 3 level. In Chapter 7, non-isothermal Alfvén wave driven wind models are calculated. It is shown that ι Aur proves to be a severe test of these models and that the transition region and the cool wind are physically separate. A brief resumé, and possible future research topics are given Chapter 8.