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We construct non-exact operator spaces satisfying the Weak ExpectationProperty (WEP) and the Operator space version of the Local Lifting Property(OLLP). These examples should be compared with the example we recently gave ofa $C^*$-algebra with WEP and LLP. The construction produces several newanalogues among operator spaces of the Gurarii space, extending Oikhberg'sprevious work. Each of our "Gurarii operator spaces" is associated to a classof finite dimensional operator spaces (with suitable properties). In each casewe show the space exists and is unique up to completely isometric isomorphism.

Operator spaces with the WEP, the OLLP and the Gurarii property