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Gate driver TPS2814 is oscillating

I posted this in a different forum but now think it should have been asked here instead.  My apologies!

I am using a pair of LM2903 comparator outputs, pulled up to 12VDC, to drive the non-inverting inputs of a TPS2814 dual MOSFET driver.  I have the outputs of the TPS2814 pulled to ground via 5.1K resistors, and using a 12V supply with .01uF ceramic and 10uF tantalum caps, close to pin 8, for bypassing.  The output for each side of the driver is tied to the inverting input of the opposite driver, because I need to make sure they're mutually exclusive--I only can allow one of these drivers to fire at a time. 

However, when the comparators alternately trigger the TPS2814 at any frequency from 1-20 Hz, I find the circuit breaks into oscillation at about 240 Hz..  I've been trying to find application notes that would show me if there is something I'm missing, but it seems from the documentation that I can connect one output directly to the other input.  Any ideas what I'm doing wrong? 

By the way, this was an intermittent issue when I breadboarded the circuit, appearing at about 20-40 Hz of trigger frequency, so I thought a good layout in a PCB would fix it.  But it made the problem much worse!  Also by the way, my circuit uses the two comparators to monitor a voltage; one triggers when the voltage rises above a deadband, and the other triggers when the voltage falls below the deadband.  The gate drivers then activate MOSFETs to raise or lower the voltage accordingly.