  We introduce the D=4 twistorial tensionfull bosonic string by considering the
canonical twistorial 2--form in two--twistor space. We demonstrate its
equivalence to two bosonic string models: due to Siegel (with covariant
worldsheet vectorial string momenta $P_\mu^{m}(\tau,\sigma)$) and the one with
tensorial string momenta $P_{[\mu\nu]}(\tau,\sigma)$. We show how to obtain in
mixed space-time--twistor formulation the Soroka--Sorokin--Tkach--Volkov (SSTV)
string model and subsequently by harmonic gauge fixing the Bandos--Zheltukhin
(BZ) model, with constrained spinorial coordinates.
