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We study a weakly local, but nonlocal model in spacetime dimension $d \geq 2$and prove that it is maximally nonlocal in a certain specific quantitativesense. Nevertheless, depending on the number of dimensions $d$, it hasstring--localized or brane--localized operators which commute at spatialdistances. In two spacetime dimensions, the model even comprises a covariantand local subnet of operators localized in bounded subsets of Minkowski spacewhich has a nontrivial scattering matrix. The model thus exemplifies thealgebraic construction of local observables from algebras associated withnonlocal fields.Comment: paper re-written with a change of emphasis and new result

String- and brane-localized causal fields in a strongly nonlocal model