wrote in message

The new appliances have the following electrical requirements:
Oven: 30 Ampere, 208/240 Volts.
Cooktop: 40 Ampere, 208/240 Volts.

Also the manufacturer recommends a time-delay fuse or circuit breaker
and a separate circuit for each.

Can I use the existing 60 amp circuit for both?

What you can (or maybe lucky to get always with) and what you should do for
ultimate safety, are different things. The manufacturer has a reason for
the requirements. I sure as hell won't tell you to try it knowing the
recommendations are different.