We consider the Adler D-function, which is defined in the spacelike region,
and the e(+)e(-) annihilation ratio smeared, according to the Poggio, Quin
n, and Weinberg method, which is determined for timelike argument. We show
that the method of the nonperturbative a-expansion allows one to describe t
hese Euclidean and Minkowskian characteristics of the process of e(+)e(-) a
nnihilation down to the lowest energy scales.