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. 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 report, 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.