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//(...)
type

  TDot = record
    X,Y:extended;
  end;

  PLine = ^TLine;

  TLine = class
    public
    A,B:TDot;
    Next:PLine;
    procedure SetAB(ax,ay,bx,by:extended);
  end;

  procedure LineListSetup;
  procedure LineListDestroy;
  procedure AddNewLine(ax,ay,bx,by:extended);
//(...)

var

  LineNewPointer,LineStartPointer:PLine;

implementation

procedure LineListSetup;
begin
  LineStartPointer:=NIL;
end;

procedure LineListDestroy;
begin
  LineStartPointer.Free;
  LineNewPointer.Free;
end;

procedure AddNewLine(ax,ay,bx,by:extended);
begin
  New(LineNewPointer);

// ### Bei diesen beiden Zeilen bekomme ich die Fehlermeldung
  LineNewPointer.SetAB(ax,ay,bx,by);
  LineNewPointer^.Next:=LineStartPointer;
// ###

  LineStartPointer:=LineNewPointer;
end;

//(...)

procedure TLine.SetAB(ax: Extended; ay: Extended; bx: Extended; by: Extended);
begin
  A.X:=ax;
  A.Y:=ay;
  B.X:=bx;
  B.Y:=by;
end;                    

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//(...)

procedure TForm1.Button1Click(Sender: TObject);
begin
  ax:=strtofloat(edit1.text);
  ay:=strtofloat(edit2.text);
  bx:=strtofloat(edit3.text);
  by:=strtofloat(edit4.text);

// Hier ist die Funktion:
  AddNewLine(ax,ay,bx,by);
end;

procedure TForm1.FormCreate(Sender: TObject);
begin
  LineListSetup;
end;