The selection gradient formula_4 determines the direction of evolutionary change. If it is positive (negative) a mutant with a slightly higher (lower) trait-value will generically invade and replace the resident. But what will happen if formula_4 vanishes? Seemingly evolution should come to a halt at such a point. While this is a possible outcome, the general situation is more complex. Traits or strategies formula_17 for which formula_18, are known as evolutionarily singular strategies. Near such points the fitness landscape as experienced by a rare mutant is locally `flat'. There are three qualitatively different ways in which this can occur. First, a degenerate case similar to the saddle point of a qubic function where finite evolutionary steps would lead past the local 'flatness'. Second, a fitness maximum which is known as an evolutionarily stable strategy (ESS) and which, once established, cannot be invaded by nearby