A strictly barrelled disk B in a Hausdorff locally convex space E is a disk such that the linear span of B with the topology of the Minkowski functional of B is a strictly barrelled space. Valdivia's closed graph theorems are used to show that closed strictly barrelled disk in a quasi- ( LB ) -space is bounded. It is shown that a locally strictly barrelled quasi- ( LB ) -space is locally complete. Also, we show that a regular inductive limit of quasi- ( LB ) -spaces is locally complete if and only if each closed bounded disk is a strictly barrelled disk in one of the constituents.