A new method is reported for minimizing the inherent fiber instability in the electrospinning process. The method, dubbed “biased AC electrospinning”, employs a combination of DC and AC potentials and results in highly‐aligned mats of polymer or composite polymer fibers. The relationship between specific processing variables such as the AC frequency and the magnitude of the DC offset was investigated and related to the resulting fiber stability and uniformity. For optimum fiber stability, the AC frequency must fall within a relatively narrow range. The upper and lower frequency limits were measured for a small group of polymers and polymer composites and were qualitatively related to solution properties and processing variables. Potential applications of well‐ordered nanofiber materials include tissue engineering, filtration, drug delivery, and microelectronics.