A process and a signal processing unit determine a pneumatic parameter (Pmus) for the spontaneous breathing of a patient. The patient is ventilated mechanically by a ventilator. A lung-mechanical model (20) and a gradient model (22) are preset. The lung-mechanical model (20) describes a relationship between the pneumatic parameter (Pmus) as well as a volume flow signal (Vol′), a volume signal (Vol) and/or a respiratory signal (Sig), which can be measured. The gradient model (22) describes a value for the pneumatic parameter (Pmus) as a function of N chronologically earlier values of the pneumatic parameter (Pmus) or of a variable correlating with the pneumatic parameter (Pmus). N values for the correlating variable are determined at first. At least one additional value is subsequently determined for the pneumatic parameter (Pmus). N chronologically earlier values of the correlating variable, current signal values, the lung-mechanical model (20) and the gradient model (22) are used for this purpose.