The invention relates to a process for preparing primary amines which comprises the process steps A) provision of a solution of a secondary alcohol in a fluid, nongaseous phase, B) contacting of the phase with free ammonia and/or at least one ammonia-releasing compound and a homogeneous catalyst and optionally C) isolation of the primary amine formed in process step B), characterized in that the volume ratio of the volume of the liquid phase to the volume of the gas phase in process step B is greater than or equal to 0.25, and/or in that the ammonia is used in process step B) in a molar ratio based on the hydroxyl groups in the secondary alcohol of at least 5:1.