The theory of a real (mixing) cascade working with constant cut number and with losses is developed. The steady-state distribution of the isotope concentrations in every stage, the total flow rate, the form factor and the number of stages for a desired final enrichment in the low concentration range are calculated. The results obtained are compared with those for the ideal (no mixing) cascade working with losses. The dynamic behaviour on the cascade is considered. A method for computing the distribution of concentrations in an arbitrary range is proposed. The thermodynamic efficiency of the separating element is determined.