This chapter takes a historical perspective on the emergence of non-linear dynamic modelling in economics. Such models, in particular, involve multistability. In the form of piecewise linearity analysis dates back to the 1930s, with study of fixed point and periodic attractors and their basins. However, even if different cases, depending on different parameter combinations, are studied, no trace of bifurcation analysis can yet be found. Quite early is also business cycle modelling, emerging around 1940, and developed into the nonlinear format around 1950. These models include forces that repel the systems from equilibria/fixed points, but are stabilized through attracting forces far out in the phase space. The resulting trajectories, limit cycles in the case of continuous time models, quasi-periodic orbits in the case of discrete time models, are, however the unique attractors. A certain awareness of Hopf/Neimark bifurcations is there, but, again, there is no explicit study of these. A particular problem for economics as a formal science is that a true study of nonlinear dynamics requires global analysis. Economics, however, has for ages been focused on equilibria and the local study of stability. This is partly due to ideological reasons, as economists preferred convex structures providing for unique equilibrium states, which could be associated with optimality. As a consequence, formal relations are usually described qualitatively, and are seldom stated in explicit form meant to hold over a wide domain of variable values. An exception is provided by production studies, where such production functions were in fact formulated and estimated from time series or panel data. They still provide the best explicit functions to use also in the study of global dynamics even though they were not developed for this purpose.