I have a 2007 Zzr 600, the gear jumps to neutral when it's on second gear. what can it be?

 

Z, glad to have you with us. What is the history of this bike? Are you the original owner? Your shifting issue could be a few things. On the limited info you've given, I might immediately suspect a slightly bent shifting fork in the tranny. However, let's back up. Have you ever inspected your clutch? What type of oil are you using? Is your clutch linkage in good tune? It's POSSIBLE (again, given the limited info) that your bike has seen some "hard shifting" prior to your ownership, and the clutch plates are worn to the point of slipping; i.e. there's not much left of the friction material to "hold them" from kicking the tranny into neutral. (Does it happen in any other gear?)
Before you assume the worst, try the easier/cheaper route. I would pull the clutch cover and the clutch "pack" to see what the plates look like. They SHOULD have about a 1/16 to 1/8th of "fiber" on them and appear like either a cork-looking material or a grey brake pad looking material. Also check the springs (probably 4 or 5 spaced like lug nuts) to see if there's still good "action" when you pull on the clutch lever. If all looks good, replace, although you might want to install a new clutch pack just to eliminate that variable. Use a fresh gasket (or, cut your own like I prefer.) If you install a new pack, SOAK the plates for about 1/2 hour before install, to make sure they're evenly introduced to the lube of choice. Use gasket goo on both sides of the gasket, and JUST snug the bolts on re-install. Let sit for about one hour. Come back and then torque to spec. DON'T overtighten and squish the goo out!
I suspect this will help some. If it does NOT, then you may need surgery to repair the shifting fork. If you're not comfortable doing this yourself (and I wouldn't advise it if you only own some pliers and screwdrivers), then you may need to take it to a shop.
It's also possible the edges of the tranny gear teeth are worn (again, from prior owner shifting like he stole it) and need to be repaired or replaced.
Try the easy stuff first, and let us know. We can probably point you in the right direction.
Welcome to KF, again. Gear up; stay safe, and easy on the shifting till you get this sorted out!

 

Welcome to KF Z

Abit more history is preferrable for sure. I too would start with the proper clutch adjustment check, and did you just change oil in the ride and with what kind?

 

Def check smallest and easiest things first. Cable adjustment? clutches? I've only been into ONE 600 motor. Damn good motor. I've seen ONE ninja with broken trans and that was an 05 636r with a guy that didnt know how to shift and did LOTS of stupid stunting with it. Messed up gear and shift fork.