A method for equilibrating biological systems such as tissues, organs or organ systems with cryoprotective agents by vascular perfusion in vitro, comprising: a) Setting a lower limit to the arterial flow rate for the perfusion process; b) Increasing the concentration of cryoprotective agents in the arterial perfusate at a constant first arterial perfusion pressure until the rising viscosity of the perfusate causes the arterial flow rate to decline to become equal to the said set lower limit to the arterial flow rate of step a); c) Holding the arterial flow rate constant at the set lower limit of arterial flow rate of step a); d) Allowing arterial perfusion pressure to rise from the first arterial perfusion pressure of step b) to a higher pressure equal to or below a preset maximum arterial perfusion pressure as a result of rising perfusate viscosity in combination with the constant lower limit of arterial flow rate of steps a) and c); and then e) Either i. continuing to perfuse the biological system at the set lower limit of arterial flow rate of step a) above, if the arterial perfusion pressure does not reach the preset maximum arterial perfusion pressure of step d) above, or, ii. if the arterial perfusion pressure reaches the preset maximum arterial perfusion pressure of step d) above, allowing arterial flow rate to fall to below the set lower limit of arterial flow rate of step a) above as may be required to maintain the arterial perfusion pressure at the preset maximum arterial perfusion pressure of step d). a) Setting a lower limit to the arterial flow rate for the perfusion process; b) Increasing the concentration of cryoprotective agents in the arterial perfusate at a constant first arterial perfusion pressure until the rising viscosity of the perfusate causes the arterial flow rate to decline to become equal to the said set lower limit to the arterial flow rate of step a); c) Holding the arterial flow rate constant at the set lower limit of arterial flow rate of step a); d) Allowing arterial perfusion pressure to rise from the first arterial perfusion pressure of step b) to a higher pressure equal to or below a preset maximum arterial perfusion pressure as a result of rising perfusate viscosity in combination with the constant lower limit of arterial flow rate of steps a) and c); and then e) Either i. continuing to perfuse the biological system at the set lower limit of arterial flow rate of step a) above, if the arterial perfusion pressure does not reach the preset maximum arterial perfusion pressure of step d) above, or, ii. if the arterial perfusion pressure reaches the preset maximum arterial perfusion pressure of step d) above, allowing arterial flow rate to fall to below the set lower limit of arterial flow rate of step a) above as may be required to maintain the arterial perfusion pressure at the preset maximum arterial perfusion pressure of step d). i. continuing to perfuse the biological system at the set lower limit of arterial flow rate of step a) above, if the arterial perfusion pressure does not reach the preset maximum arterial perfusion pressure of step d) above, or, ii. if the arterial perfusion pressure reaches the preset maximum arterial perfusion pressure of step d) above, allowing arterial flow rate to fall to below the set lower limit of arterial flow rate of step a) above as may be required to maintain the arterial perfusion pressure at the preset maximum arterial perfusion pressure of step d).