  We study both analytically and numerically phonon transmission fluctuations
and localization in partially ordered superlattices with correlations among
neighboring layers. In order to generate a sequence of layers with a varying
degree of order we employ a model proposed by Hendricks and Teller as well as
partially ordered versions of deterministic aperiodic superlattices. By
changing a parameter measuring the correlation among adjacent layers, the
Hendricks- Teller superlattice exhibits a transition from periodic ordering,
with alterna- ting layers, to the phase separated opposite limit; including
many intermediate arrangements and the completely random case. In the partially
ordered versions of deterministic superlattices, there is short-range order
(among any $N$ conse- cutive layers) and long range disorder, as in the N-state
Markov chains. The average and fluctuations in the transmission, the
backscattering rate, and the localization length in these multilayered systems
are calculated based on the superlattice structure factors we derive
analytically. The standard deviation of the transmission versus the average
transmission lies on a {\it universal\/} curve irrespective of the specific
type of disorder of the SL. We illustrate these general results by applying
them to several GaAs-AlAs superlattices for the proposed experimental
observation of phonon universal transmission fluctuations.
