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