Hi there!
I suspect that I have something that is not right in the rear swingarm. How do I check the bearings (ball and needle)?
If they are worn out, how do I replace them?

/Mats 750 Paso - 87

the swing arm bearings usually wear mainly in the ride height position...

Note: READ THIS FIRST
through this whole exercise pretend the swingarms are made from cheese...DO NOT use any levers or vices or pliers, hammers NOTHING that can damage it. The alloy is very soft and easily damaged.
while youre at it check the arm for cracks or gouges.

you mostly find that when the bike is up on a stand that there is very little play - so it's pretty useless to check in up on a stand by yourself..

get someone to sit on the bike with no stand under and put typical load on the swing arm. then push the rear of the bike sideways to apply axial [across] load on the rear wheel.
If there is noticeable lateral arm movement near the rear axle position on the arm the bearings are stuffed.
it would be good to look at the rear wheel at this time - rear wheel bearings fail too...more common on dirt bikes or if you ride thru water alot.

if you can't see movement it in the swing arm doesn't mean there is not a problem but they aren't necessarily unserviceable for general riding - depends on the degree of performance you require...

the next check to try is to remove and inspect but leave the swing arm in the bike...
chain off
brake & wheel off
shock off
try moving the swing arm up and down
feel for tight / loose spots - anything loose, it's probably stuffed
you may feel mini-clunks - this would indicate the bearing has brinelled (the rollers have marked the races or have flat spots)
if it clunks or binds - it's stuffed
check for lateral play (waggle it around)

by this stage the swing arm removal is going to be pretty simple
if you have found a problem (any of the above) it needs to come out.

the rest is a bit obvious...
it's not uncommon to find swing arm bearings rusty looking...
slightly rusty is OK but look at the rollers for flat spots and the outer race for indications of lines across - this is brinelling.
brinelling is usually caused by the impact of a round object on a flat surface - leaving a dent. In the case of swing arm bearings the races and rollers don't rotate full revolutions - in fact they hardly rotate at all - that's why they usually wear in one spot.
why do they rust???
you have an aluminium alloy swing arm and a steel frame.
the use of dissimilar metals can cause a galvanic reaction if there is and corrosion happening nearby..all the other earth points are insulated by rubber...sounds like I'm talking crap and I probably am but I have a lazy $50 says the bearing grease is chocolate brown...but this could also be fretting corrosion - where high pressure movement grinds tiny particles off the bearing faces...if the metal is discoloured brown-ish it means there has been fretting corrosion. it might be both fretting and galvanic rust...

be careful with replacement bearings.
just beacuse it "fits" [OD, ID and width] doesn't mean it's right.

with needle rollers the most common world-wide manufacturer is INA.
most bearings come with "clearance" as per the manuafacturers "standard"...this clearance is so the rollers don't skid on both races during rotation.
there are different clearances for bearings and different purposes - you need to get advice on the best precision clearance for the application from the bearing supplier if it's a non-genuine or not INA.

my advice for a good bearing lube is Lanotec grease.
you need good pressure resistance and corrosion resistance - Lanotec covers both. At least use an EP (extra pressure) grease.

before you re-assemble the whole thing check the swing arm movement in the frame.