An abstract food web, as defined in this article, consists of two parts. The first is composed of a finite set A of nodes or populations together with a mapping P of A into the subsets of A. If α is a population, then P( α) is the set of populations upon which α preys. Thus A and P determine the static structure of the food web, including the division into trophic levels. The second part of the definition determines the dynamic aspects of the web. The set of observation times T is a subset of the time axis, and S, the density function, is a mapping of T × A into the nonnegative reals. Then S( t, α) is the density of population α at time t. The major part of the article is concerned with the case where T is the interval [0, ∞) and S is given as the solution of a fairly general differential equation of the form dSα dt = SαFα(S,t) + hα(t), α ϵ A . This formulation includes the traditional Volterra equation. Under mild boundedness restrictions on certain terms in Fα, the existence of bounded solutions to (1) is established. Essentially the theorem proves the biologically obvious fact that if the population losses dominate the population gains for large population densities, then these densities must be bounded. The steady states of the autonomous form of (1) are briefly examined and a standard result in perturbation theory is applied. The general stability analysis allows us to deduce a result derived by Volterra for a much more naive model. Essentially, if two species compete for the same resource, then only one will survive. Next, autonomous food chains are investigated. Here each species preys on only one other species, and only the first is self-generating. This simplification allows us to give necessary and sufficient conditions for existence and stability of various steady states. In fact, for the case where all energy flows from populations α to populations β, with respective densities x and y, are of the form ax (1 + bx)y , disjoint intervals are found such that if the intensity of self-generation of the first species lies in any interval, then a certain steady state exists. Moreover, as this self-generation intensity increases, the number of populations (or trophic levels) present in the steady state increases. The major limitation of the theory is that most results on stability are only local, not global.