There's frequently t&m as part of a fixed-price project, owing mainly to the client's inability to foresee all his requirements at the outset. There's no t&m charge for deliverable items included in a fixed-price contract, but if something's left out, often until the "last minute" or if a significant change is suddenly required, t&m is the "easy" way to remedy that omission. Aside from that, the deliverables and processes agreed upon in a fixed-price agreement are not billed as t&m.

OTOH, some tasks are better done on t&m, particularly when there is no agreed-upon set of deliverables at the outset, or when the desired end-result is a moving target. It's not unusual to have someone say, "Gee, it would be really useful to have <this or that> included with this system." When this is late in the project, t&m is the most common way of adding a "feature," particularly if the limits of the additional item are ill-defined, not yet firmly contracted, yet impact other work within the already contracted portion of the work.

Whether the basis for billing is a fixed price, lines and connections, or time and materials, nobody is asked to pay twice for what they receive.

RE