Just bought 2013 370z

SouthArk370Z

I replace all fluids when I purchase a used car. Engine oil/filter, transmission fluid(/filter), differential fluid, coolant, washer fluid. Will replace brake fluid if it looks or smells the least bit bad.
I check the tires. As mentioned above, not just tread depth but also condition of rubber. I'll also verify that they are the correct size.
I'll grease anything that has a zerk. Have to be careful not to over do it.

If you do your own maintenance/repairs, the FSM (link in sig) is a must-have.

Edit: Other than checking electrolyte level (when possible), I don't worry too much about the battery if it still cranks strong. But if it's 6 years old, I'd set aside a few bucks for a replacement.

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Steering Lock Links - Search The370Z Bookmarklet - FSM @ NICOclub
Mankind has progressed past the need for war but we haven't evolved that far. - NachoMahma

Quicksilvers

Welcome and congratulations on your new to you Z!! I highly recommend replacing your Genuine Nissan OEM CSC with the Z Speed Performance CMAK before it fails and your Z ends up riding on the back of a flat bed tow truck I hope you have AAA good luck. I believe I am the record holder here I have replaced four Genuine Nissan OEM CSC’s before I finally installed the Z Speed Performance CMAK Kit glad I did. I definitely recommend installing an oil cooler kit before possible heat damage occurs to your engine if your Z does over heat.You will for sure want to do all your general maintenance on your Z like what was said above. Change oil and oil filter,change your transmission fluid(you will be glad you did),differential fluid,coolant,power steering fluid,and brake fluid. Check the level of your washer fluid. Check the condition of all your tires and adjust your air pressure. Check and test your battery condition.