Fickle is a class-based object oriented imperative language,
which extends Java with object \emph{re-classification}. 
In this paper, we introduce a natural \emph{observational equivalence} on
\emph{Fickle} programs. This is a \emph{contextual} equivalence on \emph{main}
methods with respect to a given sequence of class definitions, i.e. a program. 
To study it, we use the formal computational model for OO-programming based on
\emph{coalgebras}, which has recently emerged, whereby objects are taken to be
equal when the actions of methods on them yield the same \emph{observations} 
and equivalent next states. However,  in order to deal with {\em
imperative features}, we need to extend the original approach of H.Reichel 
and B.Jacobs in various ways. 
In particular, we introduce a
\emph{coalgebraic} description of objects (states of a class), which induces 
a \emph{coinductive behavioural equivalence} on programs.
For simplicity, we focus on Fickle \emph{objects} whose methods do not take
more than one object parameter as argument.  Completeness results as
well as problematic issues arising from \emph{binary methods} are also
discussed.

Keywords:
Imperative class-based OO-programming,  observational 
equivalences, coalgebraic semantics, coinductive behavioural equivalences.