Two classes of transient disturbances evident at stratospheric levels, extratropical planetary waves of gravest scale and equatorial modes confined to the tropics, are discussed theoretically and observationally. Both are briefly reviewed and developed within the framework of a space-time spectrum. This representation is a complete and, in some instances, more transparent description than the evolving physical-space analogue. It serves to reconcile the extensive modal structures emergent from observations with localized episodic descriptions. In particular, a localized transient disturbance is shown to correspond to a spectrum of modes. The transient response to localized unsteady forcing involves two constituents: a 'projection response' scaling according to the source and a normal mode or 'barotropic response' appearing at eigenfrequencies independently of forcing details. For convective heating localized in the tropics, disturbances of the first category are trapped latitudinally about the equator, but radiate vertically. In contrast, disturbances of the second category disperse laterally well out of the tropics, but are vertically trapped. Interference between traveling and stationary components is capable of inducing vacillations in eddy transports via modulation of the stationary zonal wave. In this process, the steady stream of wave action due to the stationary wave alone is transformed into one which is corpuscular and pulsating. These fluctuations, in turn, induce a vacillatory response in the basic flow, locally and intermittently, in proportion to convergences of Eliasen-Palm flux. The traveling wave event of January 1979 is re-examined in the context of a spectrum of modes or, equivalently, a dispersive wavepacket. While in general several modes are indicated, it is demonstrated that two modes, one symmetric and the other antisymmetric about the equator, are reasonably successful in characterizing the observed disturbance. Fluctuations simultaneously observed in the mean flow at upper levels are identified with the vacillatory response to modulation of the stationary wave by the traveling wave. The space-time spectrum and related considerations are applied to satellite and radar observing platforms. Advantages and limitations of each observational technique in monitoring transient phenomena are developed.