A control device of a piston pump unit comprising at least two piston-cylinder units that operate in a phase-shifted manner for the purpose of liquid chromatography and to a piston pump unit is described. The control device corrects fluctuations of the system pressure while switching from one piston cylinder unit to the respective other piston cylinder unit. The fluctuations can occur as a result of the cooling of the liquid medium that is heated in an adiabatic manner during a pre-compression phase in the working piston. The control unit controls the piston speed of at least one piston-cylinder unit during the transition phase depending on at least one characteristic, which is ascertained from chronologically previously detected pressure values, such that variations of the system pressure as a result of the cooling of the adiabatically heated medium are at least partially compensated for.