I'm using two different hard drives both with firewire connecting cables. Will I be able to connect these to the new iMacs?

Welcome to the Apple Support Communities.

For each FireWire drive you'll need these adapters:

• Apple Thunderbolt to FireWire Adapter - Apple
• Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter - Apple

If these drives still use FireWire, that indicates they are quite old and could fail soon. I'd replace the drives ASAP!

Jack

No because the FireWire to Thunderbolt 2 adapters, will not plug directly into the new iMac’s USB-C/Thunderbolt ports.

What FireWire external drives do you have?

Many of those older FireWire enclosures had both FireWire and USB connections. If your external drives have both and you still have the USB-A cables. Then you can connect those drives using the USB-A cables and a couple of USB-A to USB-C adapters.

Because new Macs use TB3, which is not backwards compatible with TB1/TB2.

You’re welcome.