Yes in both cases.
The first case is visible when an object's instantaneous velocity is 0 but its acceleration has a non-zero value. This occurs when velocity and acceleration are in opposite directions. Its is visible when an object is thrown upwards. There comes a point where it is stationary in the air with velocity 0; however, the acceleration due to Earth's gravity is still acting on it.
An object traveling at constant velocity has 0 acceleration.