Zeners - 2.4 - bad batch?

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I have a batch of 12 Zeners 2V4 - and they all exhibit a strange behaviour. A Zener will typically pass no current until it reaches its breakdown point and then it will start to conduct, and the voltage will remain more or less constant. However those 2.4V Zeners, they conduct immediately at any tiny voltage and then the voltage increases until it goes past 2.4V and keeps rising. Any ideas what I am looking at?
 
Looks normal:
http://www.nxp.com/documents/data_sheet/BZX79.pdf
They are the lowest voltage in the series, and low voltages zeners tend to have dismal characteristics: at 1V, they already pass 50µA, and their dynamic resistance at 1mA is between 275 and 600 ohm.

They could be called "Slightly Non-Linear Resistors" instead of zeners.

At these voltages, stabistors perform probably a little better: the theoretical dynamic resistance for this voltage would be in the region of 150 ohm.
 
I have now used a yellow LED followed by a 1N4148 to get the voltage drop - as shown here. I added the 1N4148 because the sinusoidal looked crooked on the oscilloscope without it.
 

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