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 | Check to make sure the U bolts or strap and bolts are tight. Look also to see that the bearing caps have retained a tight fit into their respective yokes on the driveshaft. A cap that has lost its press fit will typically have a clean, polished area on the end from spinning in the bore of the yoke. This is also a good time to look for things like a dented or twisted tube, missing balance weights, crud on the driveshaft and anything else that could cause a vibration problem.
Now, you'll want to check the attaching yokes. Are they securely attached to the transfer case or differential? Often, the nut on either of these yokes will begin to back off. If this is the case, you will be able to see the yoke move independently of the output shaft or the pinion shaft. Be careful in your diagnosis here, though, as the symptoms may be a result of bearing wear. To arbitrarily tighten the nut will usually accelerate the failure of a worn bearing. If you discover the yoke is loose, it may be a good time to drain the gearbox for a thorough inspection of the oil to look for excessive metal contamination. In the event of a bearing failure, the oil will typically have a glittery appearance. |  |
 | If you are lucky enough to have grease fittings in your U joints, use them! You should always grease until you see clean grease coming out of all four of the seals on the Universal joint. It is an urban myth that this purging will damage the seal. They are designed to purge. I recommend that you do this every time you change your oil and when you get back from that wet, muddy four- wheeling adventure. You'll be flushing the water and grit out of the bearings.
Other than that, there may be a grease fitting on the slip yoke (female sliding component) of the driveshaft. The slip yoke and spline stub are a couple of the more expensive components in a driveshaft. I don't believe that you can ever grease it too much (the EPA may disagree) and grease is a lot cheaper than finish-machined steel parts.
Proper greasing of the slip yoke will depend on the location of the grease fitting. On most older applications, the grease fitting is in the body of the slip yoke near the area that accepts the U joint. On many newer applications or reworked driveshafts, the grease fitting is in the dust cap at the end opposite the U joint (on either type of slip yoke you will find a relief hole in a plug that is in the end of the yoke under the U joint). With the first type you need to put your finger over this hole and pump grease until you see clean grease coming out past the dust cap on the opposite end. Unless you do this, grease will simply fill the cavity in the slip yoke that is not filled with the spline stub and any excess will come out of the relief hole. With the second type, pump grease until you see clean grease coming out this relief hole. The object here is to make sure that clean grease will completely coat the wearing areas of the slip yoke and spline stub. | 
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