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When it comes to Joel Madden and Nicole Richie's relationship ... one word comes to mind. Obey!

The twosome enjoyed some alone time while strolling on Melrose Avenue in Los Angeles without their two adorable children Harlow and Sparrow.

We're loving how Joel chooses a subtle hat to make such a loud statement about his romance with Ms. Richie. Loves it!

See more of the couple hangin' tough ... after the jump.