  Both experimental and theoretical analysis of an {ultra-short} phenomena
occurring during the positive streamer propagation in atmospheric pressure air
is presented. {With tens-of-picoseconds and tens-of-microns precision, it is
shown that when the streamer head passes a spatial coordinate, emission maxima
from N$_2$ and N$_2^+$ radiative states follow with different delays. These
different delays are caused by differences in the dynamics of populating the
radiative states, due to different excitation and quenching rates.}
{Associating the position of the streamer head with the maximum value of the
self-enhanced electric field, a delay of 160$\,$ps was experimentally found for
the peak emission of the first negative system of N$_2^+$.} {For the first
time, a delay dilatation was observed experimentally on early-stage streamers
and clarified theoretically.} {Thus, in the case of second positive system of
N$_2$ the delay can reach as much as 400$\,$ps.} In contrast to the
highly-nonlinear behaviour of streamer events, it is shown theoretically that
emission maxima delays linearly depend on the ratio of the streamer radius and
its velocity. This is found to be one of the fundamental streamer features and
its use in streamer head diagnostics is proposed. Moreover, radially-resolved
spectra are synthetized for selected subsequent picosecond moments in order to
visualize spectrometric fingerprints of radial structures of N$_2$(C$^3\Pi_u$)
and N$_2^+$(B$^2\Sigma_u^+$) populations created by streamer-head electrons.
