  We discuss whether the enhancement in the diphoton final state at $M_{\gamma
\gamma}$ = 750 GeV, observed recently by the ATLAS and CMS Collaborations could
be a neutral pseudoscalar technipion $\tilde{\pi}^0$. We considered two
distinct minimal models for the dynamical electroweak symmetry breaking. Here
we concentrate only on two-flavor vector-like technicolor model and we assume
that the two-photon fusion is a dominant production mechanism. We include
contributions of $2 \to 1$, $2 \to 2$ and $2 \to 3$ partonic processes. All the
mechanisms give similar contributions to the cross section. With the strong
Yukawa (technipion-techniquark) coupling $g_{TC} \simeq 20$ we roughly obtain
the measured cross section of the "signal". With such value of $g_{TC}$ we get
a relatively small total decay width $\Gamma_{\rm tot}$. We discuss also the
size of the signal at lower energies (LHC, Tevatron) for $\gamma \gamma$ final
states, where the enhancement was not observed. We predict a measurable cross
section for neutral technipion production associated with one or two soft jets.
The technipion signal is compared with the Standard Model diphoton background
contributions. We observe the dominance of inelastic-inelastic $\gamma \gamma$
processes. We predict the signal cross section for purely exclusive $p p \to p
p \gamma \gamma$ procesess at $\sqrt{s}$ = 13 TeV to be about 0.2 fb. Such a
cross section would be, however, difficult to measure with the planned
integrated luminosity. We conclude that in all considered cases the signal is
below the background or/and below the threshold set by statistics although some
tension can be seen.
