Naomi Watts & Liev Schreiber Photographed After Breakup

If Liev Schreiber and Naomi Watts look totally settled into the single life, it's because they've been at it for almost a year ... even though they just announced their breakup.

The "Ray Donovan" star looked pretty chill riding his bicycle Monday in NYC -- while Naomi, and her little dog, took a stroll in the city within a few hours of going public with the split.

Sources told TMZ the 11 year relationship was on the rocks way back in January. In fact, we were told they were already living separately in NYC, and had worked out co-parenting arrangements. Reps for Naomi and Liev denied there was trouble, and pointed to the fact they went to the Oscars together in February.

That's the thing about Hollywood appearances ... sometimes they're just that.