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In this paper we undertake an analysis of the eigenstates of two nonself-adjoint operators $\hat q$ and $\hat p$ similar, in a suitable sense, tothe self-adjoint position and momentum operators $\hat q_0$ and $\hat p_0$usually adopted in ordinary quantum mechanics. In particular we discussconditions for these eigenstates to be {\em biorthogonal distributions}, and wediscuss few of their properties. We illustrate our results with two examples,one in which the similarity map between the self-adjoint and the nonself-adjoint is bounded, with bounded inverse, and the other in which this isnot true. We also briefly propose an alternative strategy to deal with $\hat q$and $\hat p$, based on the so-called {\em quasi *-algebras}.

Coordinate representation for non Hermitian position and momentum operators