I replaced the fan motor on the condensing unit. The motor says it does not require a capacitor. When I install the fan wire into the existing capacitor the fan runs continuously. Can the capacitor be eliminated?

Just connect it without the capacitor. Should go through a relay controlled by the thermostat or control board.

Just connect it without the capacitor. Should go through a relay controlled by the thermostat or control board.

There is no wiring diagram left to view unit is very old. What should I be looking for?

If it is a 1 speed motor without a capacitor, find the incoming supply line and connect hot(usually black) to one terminal and neutral(white) to the other. If it rotates the wrong way, reverse leads. If there is more than 2 terminals you may have a 2 speed motor and will have to determine what wire combination provides the best speed is best for your system.

Sounds like you have the wrong motor for your condenser. Every condenser fan motor requires a run cap. If you can prove otherwise, I will have learned something today.