This chapter discusses qualitative methods for systems of two coupled first-order nonlinear differential equations. In most cases, these systems cannot be solved analytically. As in Chap. 3 , the aim is to describe the behaviour of the system and sketch solutions, but in this case the solutions are visualised using a two-dimensional phase plane. There are several useful techniques that help with the construction of the phase plane. Applications, described through worked examples, include models for competition between different species, the motion of a pendulum, and the growth and eventual decline of an epidemic.