They are parallel. " It's illogical to expect that they be the same tense. One is referring to what they won't do in the future: They don't intend to enter into a secret agreement.
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AnonymousWhat do you think of: The parties acknowledge that they have never entered into a secret agreement, nor do they have any such intention.No problem.
AnonymousThe parties acknowledge that they NEITHER intend to enter, NOR have they entered, into a secret agreement.I suspect you may actually be reacting to the fact that the word "they" precedes the word "neither" but does not precede "nor". (The inversion is necessary after "nor", so the word "they" must be where it is.)