Where in the world are you? That might be some help in identifying what you have.

Have you tried spraying them with Insecticidal Soap?

Perhaps scale insects. Difficult to know for certain. Portulaca is a seasonal plant. If a nasty pest, get rid of plant.

Enlarging the photo confirms scale. If only on a few stems, cut the affected ones off. Otherwise, as Jean suggests, just toss and replace.