Options.Mouse.ColumnSizing := True => no effect.

GridLines.Options.Mouse.ColumnSizing   := True;

I treat to set this option, at design time and at run time. It has no effect on a TTMXFMXGrid. 

The columns can't be resized at runtime!!!!!!!

Did you also set GridLines.Options.Mouse.FixedColumnSizing := True

The ColumnSizing property is used for the non-fixed cells only.

Can you, please, say me in which page of the documentation describes this limitation?

Where do you see a limitation? And why should it need an explanation? The properties are self-explanatory

FixedColumnSizing: enable or disable sizing on the fixed column area

ColumnSizing: enable or disable sizing on normal column area (non-fixed columns)Pieter Scheldeman2016-06-22 18:30:52

These are the properties of my Grid:

The rest are by default:
GridLines.UseColumns        := True;
GridLines.FixedColumns      :=  1; 
GridLines.FixedRightColumns :=  4; {These are the buttons on each line}
GridLines.ScrollMode        := smCellScrolling;
GridLines.RowCount          :=  1;
GridLines.DefaultRowHeight  := 20;
GridLines.BitmapContainer   := FView.BitmapContainer;
GridLines.Options.Bands.Enabled        := True;
GridLines.SelectionMode                := smSingleRow;
GridLines.Options.Borders.CellBorders  := bVertical;
GridLines.Options.Editing.Enabled      := False;
GridLines.Options.Mouse.DirectEdit     := True;
GridLines.Options.Mouse.ColumnSizing   := True;
GridLines.Options.Sorting.FixedColumns := True;
I've added GridLines.FixedColumnSizing := False;
and don't works ever!!!

really  GridLines.Options.Mouse.FixedColumnSizing := False;

I want "FixedColumns" really fixed. 

And the rest of columns sizable.

Controlling what columns can be sized is done via OnCanSizeColumn()
Controlling from which area in the grid a column can be sized is done via grid.Options.Mouse.FixedColumnSizing,grid.Options.Mouse.ColumnSizing,

Read documentation:
page 10,11 about ColumnSizing / FixedColumnSizing
and page 29 about OnCanSizeColumn