This paper continues an earlier study by S. A. Maslowe of inviscid asymmetric disturbances to flow with rotation along a pipe. It is shown that there is a class of neutral modes with a critical layer near the wall of the pipe when the azimuthal wavenumber is large and negative. Analytic and numerical properties of these modes are studied and found to lead to consistent results, notable among which is the severe singularity in the disturbance velocity at the critial level. Some of the properties of the most unstable modes are also examined.