Should my Z drive like this?

RCT... I have a pre-facelift Z (2004 3.0i) with Michelin Pilot Sport PS2 ZP's. These are the replacements I chose for the original Bridgestone RFT's. The Bridgestones were total crap. The Michelins have stopped the tramlining and most of the harsh ride. I don't believe this is your problem. Like a few on here have said, check your tire pressures and get a balance/alignment done.
I had the "Sticky Steering" issue with my Z and had the steering column replaced, problem solved with that. Your coupe does not fall into this category since it's not pre-facelift.
 
I too have Michelin's PS2 ZP tyres - they DO NOT tramline at all, never have done.

I would suspect alignment or tyre pressures - or front control arm Bushes.

Alot of people on here tend to bunch all RFT technology as the same - ie cr*p.... but have only ever tried the Bridgestone's which really are cr*p.

Fortunately there are getting to be more of us with Michelin ZP tyres who have experience of both.
 
Also check the front wishbone rear bushes as this was the primary cause of mine having a mind of its own because if they're worn, will also cause the car to wander
 
'Sticky steering' can also occur if the DSC / ABS comp systems have not been properly re-set. If that is the case, it will usually be accompanied by some yellow warning lights on the dash. If so, it takes about 15 min to reset the steering wheel comp setting, and the problem goes away.
 
I had chronic tramlining which was cured completely with non RFT Falkens, a 4 wheel alignment, suspension examination (which was all good) and lubrication of the steering column UJ's which were dry. Since all the Michelin users say they don't tramline try the other stuff first.
 
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