Persephone wrote in message
I have them all over the garden; have moved them; have taken
"pups"
to plant elsewhere. They seem to do well --for a while. Then the
leaves get ragged-looking after the flower fades. Is this normal?
Or
should the same plant bloom again later?

I will post a picture if need be, but meantime have found this site:

http://www.bromeliads.co.nz/lightshade.html

that has a plant much like mine. It is Aechmea Fasciata "Morgana".

Can anybody comment on whether I should pull up the ragged-looking
ones -- or will they bloom again?

I don't know specifically about that type of Brom but the ones I have
are all reported to die after flowering although they may produce pups
for a few years after flowering and before they die.