Most of the time Oxygen sensors get tired and worn out from old age, and they just don't respond fast enough. Here is an example of this on an 89 Chevrolet 7.4L with 93k miles.

In this display the signal shows switching, but it won't get below 200mv. Rise time from lean to rich is slow, over 200ms. I'd say this sensor is pretty weak.

After replacing the sensor, this is the waveform produced. It shows nice switching, good peak to peak voltage, good rise time, down to less than 100ms. The Computer now has good control of the system, and can provide good fuel economy and tight emission control.

Here is a superimposed image of the two signals that offers a good comparison of good vs. bad. This vehicle would not pass emission testing before the sensor was replaced.