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The purpose of this work is to study the isomorphic classifications of banach spaces c [0,'EPSILO']'TETA'c (k) and c ([0,'EPSILO'], c (k)), where 'EPSILO' is a ordinal number and k is a compact space. Essentially we consider the following compact spaces: the interval of real numbers between 0 and 1 (k=i), the alexandroff compactification of one discrete set 'TAU' (k='GAMA'TAU') and the stone-cech compactification of one discrete set 'TAU' (k='BETA'TAU'). We also develop some results about the isomorphic theory of banach space c [0,'EPSILO']'TETA'x and c ([0,'EPSILO'], x), where 'EPSILO' is a ordinal number and x is a banach space