  We develop the theory of compound functional differential equations, which
are tensor and exterior products of linear functional differential equations.
Of particular interest is the equation $\dot
x(t)=-\alpha(t)x(t)-\beta(t)x(t-1)$ with a single delay, where the delay
coefficient is of one sign, say $\delta\beta(t)\ge 0$ with $\delta\in{-1,1}$.
Positivity properties are studied, with the result that if $(-1)^k=\delta$ then
the $k$-fold exterior product of the above system generates a linear process
which is positive with respect to a certain cone in the phase space.
Additionally, if the coefficients $\alpha(t)$ and $\beta(t)$ are periodic of
the same period, and $\beta(t)$ satisfies a uniform sign condition, then there
is an infinite set of Floquet multipliers which are complete with respect to an
associated lap number. Finally, the concept of $u_0$-positivity of the exterior
product is investigated when $\beta(t)$ satisfies a uniform sign condition.
