The nonreciprocal propagation of rotationally symmetric TE-modes along a circular guide, uniformly filled with latching ferrite magnetised azimuthally to remanence, is studied theoretically. The boundary-value problem is solved in terms of Kummer confluent hypergeometric functions of complex parameter and variable. An asymptotic method for solution of the characteristic equation is developed, providing a basis for numerical computation of the eigenvalue spectrum and phase characteristics of the structure with a fair degree of engineering accuracy. The normalised nonreciprocal phase characteristics and the differential phase shift of the waveguide under rotationally symmetric TE-mode excitation are presented for both latched states of ferrite remanent magnetisation. The potentialities of the structure as digital nonreciprocal phase shifter and/or bistable ferrite switch using intrinsic advantages of ferrite remanent magnetisation are discussed.