Gamma-ray emission from the Crab Nebula has been recently shown to be unsteady. In this paper, we study the flux and spectral variability of the Crab above 100 MeV on different timescales ranging from days to weeks. In addition to the four main intense and day-long flares detected by AGILE and Fermi-LAT between 2007 September and 2012 September, we find evidence for week-long and less intense episodes of enhanced gamma-ray emission that we call "waves." Statistically significant "waves" show timescales of 1-2 weeks, and can occur by themselves or in association with shorter flares. We present a refined flux and spectral analysis of the 2007 September-October gamma-ray enhancement episode detected by AGILE that shows both "wave" and flaring behavior. We extend our analysis to the publicly available Fermi-LAT data set and show that several additional "wave" episodes can be identified. We discuss the spectral properties of the 2007 September "wave"/flare event and show that the physical properties of the "waves" are intermediate between steady and flaring states. Plasma instabilities inducing "waves" appear to involve spatial distances l ~ 10 super(16) cm and enhanced magnetic fields B ~ (0.5-1) mG. Day-long flares are characterized by smaller distances and larger local magnetic fields. Typically, the deduced total energy associated with the "wave" phenomenon (E sub(w) ~ 10 super(42) erg, where E sub(w) is the kinetic energy of the emitting particles) is comparable with that associated to the flares, and can reach a few percent of the total available pulsar spin-down energy. Most likely, flares and waves are the product of the same class of plasma instabilities that we show acting on different timescales and radiation intensities.