In the first part of this note we show that if X is a paracompact Hausdorff space and there is a locally compact closed subspace Y of X such that for every x ∈ X Y there exists an open neighborhood Ox of x in X such that Ox is base-paracompact, then the space X is base-paracompact. In the second part of this note we introduced notions of monotonically base-paracompact (base-metacompact, base-Lindelöf) and discuss some of their properties.