A magnet system known as Hybrid III under construction at the Francis Bitter National Magnet Laboratory, is described. The superconducting magnet will consist of a Nb/sub 3/Sn magnet surrounded by a NbTi magnet. In a departure from earlier design philosophy, the NbTi magnet is not designed to be cryostable; it is provided with only enough cooling to cope with nominal dissipations generated by joints and field sweeps. The magnet is therefore referred to as a quasi-adiabatic magnet. The aim of the quasi-adiabatic concept is to make a magnet sufficiently adiabatic that there will not be hot spots in the event of a quench, and yet cooled well enough to ride out steady dissipations. The cryostat can operate at 1.8 K and at 4.2 K. The superconducting section is designed to generate 13 T at 1.8 K. The system is to reach 35 T, or perhaps more as water-cooled inserts are developed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>