I have a 15 amp GFCI outlet that is connected to a 15 amp outside breaker. When using electrical items on the circuit, my outside breaker is tripping without the inside GFCI breakers tripping. I am wondering whether the outside breaker is faulty or should be 20 amps. It doesn't make sense to me that the GFCI breakers are not tripping but the outside one is. Please help.

GFCI will only interrupt current if the current going out of the outlet is not equal to that coming in by some set percentage. So if you have a 15 Amp GFCI it will trip when overloaded usually 150% of rating or when something like .5 amps difference from going out to coming back to nuetral. A regular 15 amp breaker will only trip when loaded to usually 150% of its rating. This could be very different based on long time trip setpoint and short time, this is a design of the breaker. I would need more info to help you fully. Does the outside breaker trip when the load first starts or when the load has run for a while? What model breakers are they and what are the trip settings? It sounds like you are experiencing an over load condition for the breaker outside, breakers do go bad but verrrryyy rarely. Is this a new system you have put in? If so were both breakers put in at same time?

I think you are calling the outside "breaker" a 15 A rated GFCI and the inside "breaker" a 15 A breaker. If this is the case a GFCI means a Ground Fault Circuit Interrupter and will not trip when a circuit is overloaded. The 15 A rating of the GFCI means that you can plug in a item that draws 15 A without damaging the receptacle. They trip for different kinds of faults. "Overloaded" means drawing in excess of 15 Amps. Breakers are not exact. Time and the amount of overload determines whether the breaker will trip.

20 A services usually require 12AWG wire. 15 A 14 AWG. The breaker should not be changed without changing the wire as well.

BTW, if two standard breakers are in series they may, or may not trip simultaneously.

Thanks for both the responses. Tanndog, the breaker outside only trips after the load has been on for awhile. The load that is tripping the outside breaker is a hottub circulation pump and/or inline heater. I also figured out that my garage is on the same GFCI breaker, and I have a full size refrigerator running on that circuit in the garage. It sounds like the loads, when going at the same time, are too much for the circuit and are tripping the outside breaker. Perhaps I could unplug the refrigerator, run the tub, and see if the same thing happens? That may tell me something about the load. This circuit is not a new install. It came with the house that I purchases 12 years ago. But, I recently put in the tub and started experiencing this problem. The breaker specs are as follows:
Brand looks like SA
1 pole type MP-T
MAX.RMS.SYM.AMPS
10,000 120/240 VAC
HACR type
14-10 gauge