  In this thesis the properties of two kinds of non-uniform random recursive
trees are studied. In the first model weights are assigned to each node, thus
altering the attachment probabilities. We will call these trees weighted
recursive trees. In the second model a different distribution rather than the
uniform one is chosen on the symmetric group, namely a riffle shuffle
distribution. These trees will be called biased recursive trees. For both of
these models the number of branches, the number of leaves, the depth of nodes
and some other properties are studied. The focus is on asymptotic results and
the comparison with uniform random recursive trees. It will be shown that the
studied properties of weighted recursive trees are close to uniform recursive
trees in many cases when the number of nodes increases. In contrast biased
recursive trees show a different behaviour but approach uniform recursive trees
depending on the parameters of the riffle shuffle distribution.
