  Conditional identity in distribution (Berti et al. (2004)) is a new type of
dependence for random variables, which generalizes the well-known notion of
exchangeability. In this paper, a class of random sequences, called Generalized
Species Sampling Sequences, is defined and a condition to have conditional
identity in distribution is given. Moreover, a class of generalized species
sampling sequences that are conditionally identically distributed is introduced
and studied: the Generalized Ottawa sequences (GOS). This class contains a
'`randomly reinforced'' version of the P\'olya urn and of the
Blackwell-MacQueen urn scheme. For the empirical means and the predictive means
of a GOS, we prove two convergence results toward suitable mixtures of Gaussian
distributions. The first one is in the sense of stable convergence and the
second one in the sense of almost sure conditional convergence. In the last
part of the paper we study the length of the partition induced by a GOS at time
$n$, i.e. the random number of distinct values of a GOS until time $n$. Under
suitable conditions, we prove a strong law of large numbers and a central limit
theorem in the sense of stable convergence. All the given results in the paper
are accompanied by some examples.
