A process for preventing the transfer of harmful organisms of zooplankton including the epifauna thereof and of phytoplankton including its resting stages, which are taken up with the ballast water of ships and transferred to another locality on discharge. The organisms are substantially destroyed by the addition of an agent containing a water-soluble percarboxylic acid with 1 to 6 carbon atoms, particularly an aqueous solution containing peracetic acid and/or performic acid and hydrogen peroxide, in a quantity of 0.1 to 200 mg of percarboxylic acid per liter of ballast water and allowing it to react before discharge. In a preferred embodiment, cyanide is also added to the ballast water.