AbstractWe discuss observations of Sagittarius A* with NACO@VLT in K-band and recent synchronous observations with NIRC2@Keck II and OSIRIS@Keck I in L′-band and H-band, respectively. The variability of Sagittarius A* in the near infrared is a continuous one-state process that can be described by a pure red-noise process having a timescale of a few hours. We describe this process and its properties in detail. Our newest observations with the Keck telescopes represent the first truly synchronous high cadence data set to test for time variability of the spectral index within the near infrared. We discovered a time-variable spectral index that might be interpreted as a time lag of the L′-band with respect to the H-band.