It would help to know the year of your vehicle. If it is a 280, there is a white plastic vacuum tank located low on the passenger side of the engine. The input is a vacuum source on the intake manifold. The output goes through two vacuum solenoid valves, that eventually send vacuum to the interior switch on the dash.
What you describe is almost certainly a vacuum leak. Under acceleration, vacuum in the intake manifold decreases closer to atmospheric pressure. The purpose of the vacuum tank is to provide a reservoir of vacuum for exactly those times. I suspect you have a leak under the hood in the system I just described. Pay particular attention to verify that the vacuum tank is both getting the vacuum it needs and can hold that vacuum.
I don't know how the later ZXs are set up - I'm sure others in the forum can help with that.
Tom is quite correct, it's a safe bet that the problem is a vacuum leak. On the ZX the vacuum canister is a black, stubby sort-of-cylinder on the passenger side engine compartment near the front of the engine, just to the left and behind the coolant overflow container. It is black, has several vacuum lines leading into it and has a few electrical connections. Two of the vacuum lines go through the firewall into the passenger compartment on the passenger side, between the engine and the battery tray.
Good money says that one of these vacuum lines is your problem. Check all of them and replace with line from your local parts store (cheap). While you're at it, you may want to inspect ALL the underhood vacuum lines and replace as necessary too. It's easy, cheap and will save you consternation later. Especially examine the ones near the intake manifold (heat destroys them eventually) and the cruise control booster vacuum lines.