  We study the evolution of entanglement of a pair of coupled, non-resonant
harmonic oscillators in contact with an environment. For both the cases of a
common bath and of two separate baths for each of the oscillators, a full
master equation is provided without rotating wave approximation. This allows us
to characterize the entanglement dynamics as a function of the diversity
between the oscillators frequencies and their mutual coupling. Also the
correlation between the occupation numbers is considered to explore the degree
of quantumness of the system. The singular effect of the resonance condition
(identical oscillators) and its relationship with the possibility of preserving
asymptotic entanglement are discussed. The importance of the bath's memory
properties is investigated by comparing Markovian and non-Markovian evolutions.
