During combat, if at least one attacking or blocking creature has First Strike or Double Strike as the combat step begins, the only creatures that assign combat damage in that step (the additional damage step) are those with First Strike or Double Strike.
After that step, instead of proceeding to the end of combat, the phase gets a second damage step (the basic damage step) . The only creatures that assign combat damage during the basic damage step are the remaining attackers and blockers that had neither First Strike nor Double Strike as the additional combat damage step began, as well as the remaining attackers and blockers that currently have Double Strike. After that step, the phase proceeds to the end of combat step.
If no creature has First Strike or Double Strike during combat, the only combat damage step is the basic damage step.