The Mueller matrix calculus is used to derive signal equations for a technique for nanosecond time-resolved magnetic circular dichroism (TRMCD) spectroscopy that is based on detection of the polarization state of highly eccentric, elliptically polarized light. These equations link the observed signal to the magnetic circular dichroism of the sample in the presence of measurement artifacts associated with imperfect optical devices and the birefringence induced in laser-photolyzed samples by photoselection. The results provide a methodical basis for optimization of optics and artifact reduction. An experimental example of the most important artifact, arising from the second-order coupling of birefringence and Faraday rotation, is presented for the case of laser-photolyzed (carbonmonoxy)myoglobin. The first-order linear birefringence artifact previously identified in ellipsometric measurements of natural CD cancels from magnetic CD spectra obtained as the difference of opposed field-polarity measurements, an important advantage for fast and ultrafast TRMCD studies of photoinitiated molecular processes.