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Research on coherent structures in cylindrical pipes is an area of much recent activity. Of particular interest are traveling wave (TW) states at large Reynolds number R. The existence and stability of these states, and their connection in phase space play important roles in understanding both transition and large R behavior of pipe flows. In this talk, we consider possible asymptotic structures at large Reynolds number R and identify numerically calculated solutions as finite R realisation of a nonlinear viscous core (NVC) state that collapse towards the pipe center with increasing R at a rate R^{-1/4}. We also identify previous numerically calculated states as finite R realisation of a vortex wave interacting (VWI) state with asymptotic structure similar to the ones in channel flows studied earlier by Hall & Sherwin (J. Fluid Mech., vol. 661, 2010, pp. 178–205). In addition, stability features of both VWI and NVC states are investigated. Numerical calculations confirm lower-branch travelling waves have slow and low dimensional unstable manifolds suggesting their relevance to transition in turbulence.