In modelling physical systems it frequency turns out that only the so-called singular (also termed descriptor or implicit in the literature) form of the state equations can be obtained. Then the derivative of the state vector for the continuous case or the next value of the state vector for the discrete case is pre-multiplied by a square singular (or even rectangular) matrix. Such models have more complex structure than their standard (also termed non-singular in the literature) counterparts with subsequent implications in terms of, for example, controller design. Note, however, that singularity is also useful, e.g. it can be used to derive the so-called semi-state description in cases when it is impossible to derive the state space description. In some cases, however, singularity is not an intrinsic feature of the system but is due, for example, to the effects of ‘non-adequate’ modelling or the method employed to construct the model. For a given example of this last case, a standard model may exist but is very difficult to construct. One way of avoiding singularity is to apply (if possible) well established algebraic transformations to the state vector. In this paper, an overview of recent results on singularity of equivalent state space realizations of 2D linear systems and methods for avoiding this property is given. For example, the role of inversion and bilinear transformations in the latter respect are treated together with singularity of the so-called linear repetitive processes and the introduction of this property as the result of discretization.