Models of computational devices represent one of the main formalizations of the notion of computability. Proceeding from Recursion theory to Complexity theory and Algorithmics notions of time and space consumed during a computation become relevant. These notions however are highly model dependent. Even with this machine dependence complexity theory has obtained a solid foundation, since the various models are found to be equivalent in their computational power, provided they are compared on a sufficiently coarse scale: the relevant comparison is given by mutual simulations with polynomially bounded overhead in time and constant factor overhead in space. The so-called Invariance Thesis expreses our faith that there exists a class of reasonable sequential devices, which all are equivalent if measured on this scale, and which capture our natural intuition for the realm of sequential computation. An alternative class of models is formed by the parallel models. Parallelism comes in many versions, and not all of them have been shown to be equivalent the way the sequential models are. A prominent subgroup among the parallel models is the so-called Second Machine Class, consisting of those parallel machine models that satisfy the parallel computation thesis. These models are characterized by the right balance between exponential growth pattern on the one hand, needed to make them PSPACE powerful, and uniformity of behavior on the other hand in order to prevent (in particular their nondeterministic version) to become too powerful. There exist in the literature a number of sequential models that have the property that they can recognize in polynomial time exactly what a Turing machine can recognize in polynomial space. These models therefore belong to the Second Machine Class. Models of this sort have been studied in the literature over the past 22 years. In my talk I will present two examples of such models which are not well known in the literature. The two models presented in this talk share the property that they are conceptually very close to the standard first class sequential models which are computationally equivalent to Turing machines. The first model, called the EDITRAM is obtained as an abstraction of a text editor. The second model is a parallel version of the storage modification machine. This model, called the Associative Storage Modification Machine (ASMM) is the first machine model based on pointer manipulation which achieves this complexity status. The associative Storage Modification Machine obtains its computational power from following pointers in the reverse direction.