  Erd\"{o}s-Hajnal conjecture states that for every undirected graph $H$ there
exists $ \epsilon(H) > 0 $ such that every undirected graph on $ n $ vertices
that does not contain $H$ as an induced subgraph contains a clique or a stable
set of size at least $ n^{\epsilon(H)} $. This conjecture has a directed
equivalent version stating that for every tournament $H$ there exists $
\epsilon(H) > 0 $ such that every $H-$free $n-$vertex tournament $T$ contains a
transitive subtournament of order at least $ n^{\epsilon(H)} $. This conjecture
is known to hold for a few infinite families of tournaments. In this paper we
construct two new infinite families of tournaments - the family of so-called
galaxies with spiders and the family of so-called asterisms, and we prove the
correctness of the conjecture for these two families.
