a method and apparatus for improving the acceleration behavior of a self - igniting internal combustion engine driven with an exhaust turbocharger by displacing the onset of injection during the acceleration phase toward &# 34 ; early &# 34 ;, and a combustion chamber pressure is attained , which at least in part compensates for reduction in engine power caused by sluggishness of the turbocharger and a resultant smaller cylinder charge . further increase in power is attained by means of an increase in the fuel component made possible by the adjustment of injection onset without exceeding the smoke limit of combustion . apparatus are furthermore proposed for performing the method according to the invention , in which with the aid of an acceleration signal obtained by hydraulic or electric elements an adjustment toward &# 34 ; early &# 34 ; is effected in a hydraulically functioning injection adjustment device .