Answer: Phlox can be either annual or perennial. Annual types should be deadheaded after the first flush of bloom, to encourage additional flowering. At the end of the season these plants will die. Perennial phlox should be sheared back after blooming to keep the plants neat and tidy. They will bloom over a long season, so keep the dead flowers cut off regularly. If yours is the perennial phlox, you can trim them back by about 1/3 now, or wait until spring to cut them back.
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