If you have two convictions, you should disclose both. You'd probably screw yourself if you only disclosed one and they found two.
If you're asking what your prospective employer will do, that is up to them.
In the mean time, why not get your cases dismissed (aka expunged) so you won't have to disclose them at all? A local criminal defense attorney in the county where your case(s) were can assist for a nominal fee.
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Sometimes an employer is looking for honesty as much as they are for a criminal history check. Others have a hard policy of not hiring people with certain convictions. They will certainly not hire you if you put one and they find the other. A worse scenario is getting the job, got all settled in and were then fired because the other conviction was found. I believe you did the right thing.
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It is better to disclose both.. Hopefully they are old, and not crimes of moral turpitude like a theft.. If this is for employment you should get them "expunged". I think you did the right thing and hopefully will not be out of the running.
I guess it would depend on exactly what charges they were and if they were conditional pleas or expunged or not. Also, how the application was worded is important. Do you have this info for us?