Ground the fixture to the equipment grounding conductor. It will be bare or have green insulation on the individual conductor.

Thanks, the ground wire in the cable is bare compared to the hot and neutral. My question was more about what in the fixtures is the ground connected to? I don't see an obvious screw in the fixture that would be used for that.

The grounds on the metal junction boxes used for ceiling incandescent fixtures have the grounds wrapped around the romex clamps. Is that correct for them and for clamps that I will put on the fluorescent fixtures?

Recent fluorescent fixtures have a dedicated green-colored screw for the equipment grounding conductor. In the absence of such, I would drill a hole and use a machine threaded screw, such as 10-32, with a nut on the screw where it protrudes through the fixture back.

Check, thanks very much. I have seen the green screws on other fixtures, but there is not one in this fixture which is probably ca. 35 years old.

Thanks for your advice. The two single-tube strip fixtures are operating well after years of not firing properly.

I am pleased by your success and a bit flattered that my advice was taken seriously. For the benefit of any who might still be reading, it is important that the ballast housing and the fixture housing have good contact with each other for proper functional grounding.

"In the absence of such, I would drill a hole and use a machine threaded screw, such as 10-32, with a nut on the screw where it protrudes through the fixture back."

A nut is not required if the hole is tapped (and they are supposed to be tapped).
An internal tooth lock washer under the screw head against the fixture metal will make and maintain the correct gas tight contact needed.

"metal ceiling box now has romex with the ground wires connected to the clamps"

This does not sound correct.

the box should have a tapped screw to bond the box itself, and all the ground wires (and the box bond) should be connected together using an apportioned connector (like a wire nut).

A wire to the fixture grounding screws can be added to this wire nut.

I did not describe the grounding of the basement ceiling boxes very well. The bare ground wire is wound neatly around the cable and clamped with the cable. I can not see that many of the original boxes, maybe three. They are rounded with one knock-outs on each side. The porcelain fixtures mounted them are the type to hold an unprotected incandescent bulb. They were originally controlled with one switch at the top of the stairs.

I will give you some more information so you more experienced guys can try to come up with an explanation if you want to take a shot at it. The house was built in 1959 and had cables with ground wire. The outlets were, however, with no ground. The house has seen electricians at twice to do major work since 1959. In 1970 the basement was 3/4 finished leaving a boiler room/laundry area where I was working and seeing the boxes I described. The kitchen was re-done (with the wiring done by a known dumb-ass) ca. 1985. A couple of more discrete changes were made at other times by professionals. I just looked at the original 240 dryer outlet. It has no ground, the ground wire from the cable appears to back out of the clamp, but is not wound around the cable in this case. I do not recall seeing any screw to ground to in the boxes. Maybe I should take another look.

Knowing as little as I do, I would have to hypothesize that when the house was built in 1959, it was durning a transition to grounded cabling and outlets. The boxes that were intended for outlets were left with the ground inside the box. (I wonder if the ceiling boxes on the main floor are like in the basement.) At the other boxes, the electrician did the winding thing. When basement changes were made, i am sure that those circuits were changed. the electrician should have upgraded the older boxes, but did not. (It seems like not a stellar job. I discovered that one of his boxes did not have a cover. When I looked at it closely, I discovered why. it is too full to have a cover fit! There are six cables going into a round, double box. I see my next project. Fortunately, there is enough slack to work around it and plenty of space to install a larger box.

Yes, 1959 was during the time that equipment grounding conductors were required for just some of the branch circuits, notably those in bathrooms and kitchens, perhaps basements. Boxes did not necessarily have the threaded hole for a dedicated rounding screw. The earliest of the NM cables with equipment grounding conductors often had a woven outer covering tinted a metallic green color. The grounding conductor was a smaller gauge than the other conductors.
As a practical matter, an electrician engaged to swap a fixture is not going to correct every flaw that he might find with the work done prior to his visit. The customer often refuses to pay for such. I have declined some jobs where the existing is just too bad and practical correction would require complete rewiring.
Box extensions can sometimes be used to alleviate overcrowding.

I should have typed dedicated "Grounding" screw. Push-on clips were often used for grounding the metal boxes.

"Yes, 1959 was during the time that equipment grounding conductors were required for just some of the branch circuits, notably those in bathrooms and kitchens, perhaps basements. "

Luckily, my parents got all grounded conductors which made grounded outlets easy. As for myself, it screwed me up a bit. For years, I thought that any two-conductor outlet could be easily upgrade to have a ground. It was a rude awakening when I bought a house and found that could not do that!

"The bare ground wire is wound neatly around the cable and clamped with the cable."

This was never accepted, but was all to common when grounding wires first started being used.