Tense naming question

Greetings all,
I have recently modified the language I am currently working on to
include two different past tenses. One is for actions that started in
the past, but are still happening. The other for actions that started in
the past are are no longer happening. Is there a name for these
different tenses, and if not, does anyone have any good suggestions
and/or interesting examples of naturals languages that have the same
distinction?

Thanks,
Trinsic

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