procedure TForm1.FormCreate(Sender: TObject);
begin
   // Для горизонтальной полосы прокрутки
   ScrollBox1.HorzScrollBar.Smooth := True;
   ScrollBox1.HorzScrollBar.Tracking := True;
   // Для вертикальной полосы прокрутки
   ScrollBox1.VertScrollBar.Smooth := True;
   ScrollBox1.VertScrollBar.Tracking := True;
end;

procedure TForm1.ScrollBox1MouseWheel(Sender: TObject;
  Shift: TShiftState; WheelDelta: Integer; MousePos: TPoint;
  var Handled: Boolean);
begin
   ScrollBox1.VertScrollBar.Position :=
      ScrollBox1.VertScrollBar.Position - WheelDelta;
end;

type
  TForm1 = class(TForm)
    ScrollBox1: TScrollBox;
    Panel1: TPanel;
    Panel2: TPanel;
    Button1: TButton;
    procedure FormCreate(Sender: TObject);
    procedure FormDestroy(Sender: TObject);
    procedure Button1Click(Sender: TObject);
  private
    FScrollBoxWndProc: TWndMethod;
    procedure ScrollBoxWndProc(var Msg: TMessage);
    procedure WMMouseWheel(var Msg: TWMMouseWheel); message WM_MOUSEWHEEL;
  public
    FShowHoriz: Boolean;
    FShowVert: Boolean;
  end;

implementation

procedure TForm1.FormCreate(Sender: TObject);
begin
   FShowHoriz := False;
   FShowVert := False;
   FScrollBoxWndProc := ScrollBox1.WindowProc;
   ScrollBox1.WindowProc := ScrollBoxWndProc;
end;

procedure TForm1.FormDestroy(Sender: TObject);
begin
   ScrollBox1.WindowProc := FScrollBoxWndProc;
   FScrollBoxWndProc := nil;
end;

procedure TForm1.ScrollBoxWndProc(var Msg: TMessage);
begin
   ShowScrollBar(ScrollBox1.Handle, SB_HORZ, FShowHoriz);
   ShowScrollBar(ScrollBox1.Handle, SB_VERT, FShowVert);
   FScrollBoxWndProc(Msg);
end;

// Прокрутка колесом мыши
procedure TForm1.WMMouseWheel(var Msg: TWMMouseWheel);
begin
   ScrollBox1.VertScrollBar.Position :=
      ScrollBox1.VertScrollBar.Position - Msg.WheelDelta div 10;
end;

// "Ручная" прокрутка
procedure TForm1.Button1Click(Sender: TObject);
begin
   ScrollBox1.ScrollInView(Panel2);
   // или так
   // ScrollBox1.VertScrollBar.Position := 100;
end;