Nonaxisymmetric (∂/∂&thgr;≠0) rotating equilibria are investigated theoretically for strongly magnetized, low‐density (&ohgr;pe2/&ohgr;ce2≪1) pure electron plasmas confined in cylindrical geometry. These two‐dimensional equilibria are also called rotating coherent structures, and are stationary (time independent) in a frame of reference rotating with angular velocity &ohgr;r=const about the cylinder axis (r=0). Radial confinement of the pure electron plasma is provided by a uniform axial magnetic fieldB0ez, and a grounded, perfectly conducting, cylindrical wall is located at radiusr=rw. The analysis is based on a nonrelativistic, guiding‐center model in the cold‐fluid limit (the continuity and Poisson equations) that treats the electrons as a massless fluid (me→0) withE×Bflow velocityVe=−(c/B0)∇&fgr;×ez. Within this model, general rotating equilibria with electron densityne≡nR(r,&thgr;−&ohgr;rt) and electrostatic potential &fgr;≡&fgr;R(r,&thgr;−&ohgr;rt) have the property that the electron density is functionally related to the streamfunction &psgr;R=−e&fgr;R+&ohgr;r(eB0/2c)r2bynR=nR(&psgr;R).The streamfunction &psgr;Rsatisfies the nonlinear equilibrium equation ∇2&psgr;R=−4&pgr;e2nR(&psgr;R)+2&ohgr;reB0/cwith &psgr;R=&ohgr;r(eB0/2c)rw2≡&psgr;w=const on the cylindrical wall atr=rw. Following a general discussion of rotating equilibria, an integral equation formulation of the nonlinear equilibrium equation is developed to investigate equilibria with ‘‘waterbag’’ (step‐function) density profiles. In this investigation, a numerical method is formulated that can be used to construct diverse classes of highly nonlinear waterbag equilibria. This method is employed to investigate two classes of nonaxisymmetric equilibria that are nonlinear extrapolations of well‐known small‐amplitude equilibria. These two classes of rotating equilibria bear strong similarities to coherent structures observed experimentally by Driscoll and Fine [Phys. Fluids B2, 1359 (1990)].