It is proved in [1] & [2] that a set bounded in an inductive limit   E = indlim   E n of Fréchet spaces is also bounded in some E n iff E is fast complete. In the case of arbitrary locally convex spaces E n every bounded set in a fast complete indlim   E n is quasi-bounded in some E n , though it may not be bounded or even contained in any E n . Every bounded set is quasi-bounded. In a Fréchet space every quasi-bounded set is also bounded.