  We study the existence of a periodic solution for a differential equation
with distributed delay. It is shown that, for a class of distributed delay
diferential quations, a symmetric period 2 solution, where the period is twice
the maximum delay, is given as a periodic solution of a Hamiltonian system of
ordinary differential equations. Proof of the idea is based on (Kaplan & Yorke,
1974, J. Math. Anal. Appl.) for a discrete delay differential equation with an
odd nonlinear function. To illustrate the results, we present distributed delay
differential equations that have periodic solutions expressed in terms of the
Jacobi elliptic functions.
