This paper describes test-particle simulations of the response of the outer parts of Galactic discs to barring and spiral structure. Simulations are conducted for cold Mestel discs and warm quasi-exponential discs with completely flat rotation curves, subjected to pure quadrupoles and logarithmic spirals. Even though the starting velocity distributions are smooth, the end-points of the bar simulations show bimodality and multipeaked structures at locations near the outer Lindblad resonance (OLR), although spirality can make this smoother. The growth of a bar may cause the disc isophotes to become boxy at the OLR, as stars accumulate particularly along the minor axis. The growth of a bar is also accompanied by substantial heating of the disc stars near the OLR. For the growth of a 10(10)-M. bar, the radial velocity dispersion is typically quadrupled for initially cold discs (initial sigma(u) similar to10 km s(-1)), and typically doubled for discs with final sigma(u) similar to 45 km s(-1). Simulations performed of the growth and dissolution of bars give very similar results, demonstrating that the heat once given to disc stars is very difficult to remove.