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The solar spectrophotometer “Mark-I”, located at the Observatorio del Teide and continuously operated for the last 36 years, provides high precision measurements of the radial velocity of the Sun-as-a-star. This has enabled the study of the small velocity fluctuations produced by normal solar oscillation modes and the characterization of its spectrum. Furthermore, because of its high sensitivity and long term instrumental stability, Mark-I also provides accurate daily measurements (with a precision better than 1 m/s) of the radial velocity offset, the so-called “solar gravitational red-shift” (GRS). In the present work, the first results of the analysis of this parameter over the whole period 1976–2011 are presented.