It is well-known that Abstract State Machines (ASMs) can simulate ``step-by-step" any type of machines (Turing machines, RAMs, etc.).

We aim to overcome two facts:

1) simulation is not identification,

2) the ASMs simulating machines of some type do not constitute a natural class among all ASMs.

We modify Gurevich's notion of ASM to that of EMA (``Evolving MultiAlgebra") by replacing the program (which is a syntactic object)

by a semantic object: a functional which has to be very simply definable over the static part of the ASM. We prove that very natural classes of EMAs correspond via ``literal identifications'' to slight extensions of the usual machine models and also to grammar models.

Though we modify these models,we keep their computation approach:

only some contingencies are modified.

Thus, EMAs appear as the mathematical model unifying all kinds of sequential computation paradigms.