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We have developed novel SQUID current sensors consisting of a sensitive 16-SQUID input stage followed by an output stage of 40, 160, or 640 low-inductance SQUIDs. A highly gradiometric design of the individual SQUIDs with ap 5 mum maximum linewidth makes the devices insensitive to external magnetic noise and allows cool-down and operation in the Earth magnetic field. Output current feedback (OCF) is used to increase the linear signal range. When driving a terminated 50 Omega coaxial cable, the sensor with 160 output SQUIDs exhibits a signal range of one flux quantum Phi0 at a power dissipation of about 100 nW. At 10 MHz and 4.2 K, a total flux noise level of 0.34 muPhi0/radic(Hz) is achieved corresponding to a dynamic range of plusmn 1.5 times 106 radic(Hz). At higher frequencies, interaction of preamplifier voltage noise with the output cable impedance increases the sensor noise (a general problem in high-speed SQUID systems). The small-signal bandwidth is >200 MHz. A very high slew rate of > 50 Phi0/mus is achieved allowing one to use the full signal range at frequencies up to 16 MHz with a total harmonic distortion below ap1%.