  Using the symmetry properties of the strong interaction, such as the Pauli
principle, the P-invariance, the conservation of the total angular momentum and
isotopic invariance, we establish the spin structure of the threshold matrix
elements for the processes $p+p\to \Theta^+ +\Sigma^+$ and $n+p\to \Theta^+
+\Lambda^0$, in a model independent way, which applies to any spin and parity
of the $\Theta^+$-hyperon in the near threshold region. We predict the double
spin observables for these processes, such as the dependence of the
differential cross section on the polarizations of the colliding nucleons, and
the coefficients of polarization transfer from a nucleon beam or target to the
produced $\Sigma^+$ or $\Lambda^0$ hyperon. We prove that these observables are
sensitive to the P-parity of the $\Theta^+$ baryon, for any value of its spin.
As an example of dynamical considerations, we analyzed these reactions in the
framework of K-meson exchange.
