BATSE’s Spectral Detectors provide a series of high resolution spectra over the duration of a gamma‐ray burst; fits to these spectra show the evolution of the continuum as the burst progresses. The burst continuum can usually be fit by the spectral fromAE&agr; exp(−E/kT) from ∼25 keV to more than 3 MeV, with varying trends in the value and evolution of the spectral parameters. As a result of limited statistics forE≳1–2 MeV in the individual spectra, a high energy power law is not required. Only long duration strong bursts can be studied by fitting a series of spectra, and therefore our conclusions concern only this class of burst. The bursts we analyzed tend to be characterized by a hard‐to‐soft trend both for individual intensity spikes and for the burst as a whole: the hardness (e.g.,Twith &agr; fixed) leads the count rate in spectra which resolve the temporal variations, while the hardness of successive spikes decreases. We also summarize the performance of the Spectral Detectors and the development of analysis tools to date.