We have considered so far autonomous differential systems, without delays. Delays are however known to be involved in biological systems, because for example mRNA synthesis and transport (in eukaryotic cells) are certainly not instantaneous. Delays can be a major source of instability in negative feedback circuits (the intuitive situation being that of a correction to an offending variable which is applied too late, and has increased too much by the time it becomes effective, thus causing a swing in the opposite direction of the offending variable), and have been shown to effectively cause oscillations in biological systems [52,53]. Systems with delays are however most difficult to deal with analytically, because they are differential systems of infinite dimensions, to which one cannot associate finite-dimensional Jacobian matrices. Asynchronous automata have been proposed to describe regulatory networks [54]. It should prove interesting to make use of hybrid automata (whose theory is described in [55]), derived from computer program verification techniques, the disadvantage being that differential equations have to be discretised into piecewise linear systems. Such automata are useful when some system variables are amenable to boolean treatment (which is often the case for regulating genes which have on/off states, see [56] for a discussion and the description of a boolean formalism for genetic circuits), and can easily take delays into account in simulations; programs are available to prove properties about them, for example that they can (respectively cannot) reach situations which are desirable (respectively not desirable).