Replacing my original shocks

I have a euro spec 1988 GTS 328 and it seems to me that my back end is giving in around corners. I thinking that my shocks my have to be replaced, if I do so will my handling improve. Your thoughts on improving my handling with minor changes to the car. How long do shocks usually last, it seems to hold at lower speeds around a turn but as I increase the speed it gives in. It is a unusual feeling of the cars handling characteristics, is this normal.