Honda Accord EX surges at speed

While driving at say 60 mph, the engine will rev higher and raise the rpm with out affecting the speed of the engine.

First, of all if this is correct, is the engine truelly reving or is it a false reading by the tach?

Is this an automatic or manual tranny?

Automatic transmission.

I can hear the engine RPMs increase. The actual speed and rpm surge is an estimate, but close. I do not think it is a false indication.

But bottom line is the engine does not go faster but the engine will raise in rpm. Right?

Or is the issue the unsteady spead of the engine?

Does the car have cruise and will it hold the speed steady?

Yes, it has sc. When it is engaged it holds speed steady.

The engine speeds up but the car does not accelerate.

RPMs go up from 2600 to 3000 roughly.

I have an issue with my battery, maybe the charging circuit. Could these be related?

What if the O2 heater isn't working properly????

I have to sort through this rpm increase but no speed increase. This would indicate that there is a slippage in the transmission. IF the engine surges and the transmission is fine, the car will try to speed up. It may not be overly noticeable but it should try to increase the speed. Do you agree with this? Now, is the tranny giving any other indications of slippage? Why is it the cruise can hold it steady?

The transmission was re-built about 2 yrs ago. I haven't had any problems with it. It shifts through all 3 gears just fine.

I am still confused here. You run the pedal and the car will surge the engine rpm but not the speed of the vehicle. Cruise runs the pedal and everything works fine. Right? Help me out here as there is no logic behind this.