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In this paper, we examine regularity issues for two damped abstract elasticsystems; the damping and coupling involve fractional powers $\mu, \theta$, with$0 \leq \mu , \theta \leq 1$, of the principal operators. The matrix definingthe coupling and damping is nondegenerate. This new work is a sequel to thedegenerate case that we discussed recently in \cite{kfl}. First, we prove thatfor $1/2 \leq \mu , \theta \leq 1$, the underlying semigroup is analytic. Next,we show that for $\min(\mu,\theta) \in (0,1/2)$, the semigroup is of certainGevrey classes. Finally, some examples of application are provided.

Regularity of the semigroups associated with some damped coupled elastic systems II: a nondegenerate fractional damping case