We report on the design and operation of a novel class of nonreciprocal acoustic filters operating in the radio frequency (RF) range. These devices use the spectral characteristics of commercial acoustic filters placed in angular momentum biased networks to achieve large nonreciprocity, low insertion loss (I.L.), and wideband operation. Owing to the high rejection exhibited by acoustic filters, these novel devices can achieve an unprecedented suppression of undesired intermodulation products, thus approaching the spectral purity attained by conventional linear-time-invariant (LTI) filtering components. In addition, a new analytical model suitable to capture the behavior of any angular-momentum-biased nonreciprocal device is presented. This model allows us to identify the main characteristics of the transfer function (poles and zeroes) relative to this new class of nonreciprocal filters, thus enabling new synthesis capabilities through standard numerical methods. Ultimately, the performance of a built 1.1-GHz nonreciprocal acoustic filter prototype is reported. This device relies on a modulation implemented through switched capacitors and shows I.L., isolation, and half-power bandwidth values of 4.5 dB, 28 dB, and 20 MHz, respectively, achieved through the use of a 40-MHz modulation frequency. Moreover, by showing an intermodulation distortion lower than -34 dBc, it approaches the operation of LTI circuits.