In this paper a model has been developed to investigate the propagation characteristics and gain saturation performances of novel structure tapered-waveguide traveling-wave semiconductor laser amplifiers (TTW-SLA's), which are very attractive for high-power SLA's. The influence of several physical mechanisms are analyzed: mode conversion and its polarization dependence and spatially inhomogeneous saturation (i.e., carrier hole-burning). Two taper geometries are studied in detail: the exponential TTW-SLA and the linear TTW-SLA. The first one is shown to be more efficient for narrow tapers (output width < 14-mu-m), whereas the linear TTW-SLA becomes superior for wide-taper geometries because of its better adiabatic propagation characteristics. Both tapered structures can provide a consistent improvement in the saturation output power compared to the conventional TW-SLA (approximately 9 dB for the exponential TTW-SLA and approximately 13 dB for the linear TTW-SLA), reaching absolute values in the order of approximately 18 dBm and approximately 23 dBm for the exponential and linear TTW-SLA's, respectively (a bulk semiconductor active layer is considered). The efficiency of conversion between the electrical and optical power is also shown improved by the tapered structure. The propagation characteristics for an exponential TTW-SLA have been measured (via the lateral far-field pattern) and found in reasonable agreement with the theory.