Spin correlations for the $\Lambda \Lambda$ and
$\Lambda \bar{\Lambda}$ pairs, generated in relativistic
heavy-ion collisions, and related angular correlations at the
joint registration of space-parity nonconserving hadronic decays
of two hyperons are theoretically analyzed. These correlations
give important information about the character and
mechanism of multiple processes, and the advantage of the
$\Lambda \Lambda$ and $\Lambda \bar{\Lambda}$ systems over
other ones is conditioned by the fact that the $P$-odd decays
$\Lambda \rightarrow p + \pi^-$ and
$\bar{\Lambda} \rightarrow \bar{p} + \pi^+$ serve as effective
analyzers of spin states of the $\Lambda$ and $\bar{\Lambda}$
particles -- thus, the respective spin correlations can be
rather easily distinguished and studied experimentally, which
is especially important for studies of multiple particle
generation at
modern and future ion colliders (RHIC, LHC, NICA).
The correlation
tensor components can be derived by the method of
"moments" -- as a result of averaging the combinations of
trigonometric functions of proton (antiproton) flight angles
over the double angular distribution of flight directions for
products of two decays. The properties of the "trace" $T$ of the
correlation tensor (a sum of three diagonal components),
which determines the angular correlations as well as the
relative fractions of the triplet states and singlet state of
respective pairs, are discussed.

In the present talk, spin correlations for two identical ($\Lambda
\Lambda$) and two non-identical ($\Lambda \bar{\Lambda}$) particles are generally considered from the viewpoint of the conventional model of one-particle sources. In the framework of this model, correlations vanish at enough large relative momenta. However, under these conditions (especially at
ultrarelativistic energies), in the case of two non-identical particles ($\Lambda \bar{\Lambda}$) the two-particle --
quark-antiquark and two-gluon -- annihilation sources start playing a noticeable role and lead to the difference of the
correlation tensor from zero. In particular, such a situation may arise, when the system passes through the "mixed phase" and -- due to the multiple production of free quarks and gluons in the process of deconfinement of hadronic matter -- the number
of two-particle sources strongly increases.