<DataGrid AlternationCount="2">

   <DataGrid.RowStyle>

        <Style TargetType="{x:Type DataGridRow}">

            <Style.Triggers>

                <Trigger Property="ItemsControl.AlternationIndex"

                         Value="0">

                    <Setter Property="Background" Value="Red" />

                </Trigger>

                <Trigger Property="ItemsControl.AlternationIndex"

                         Value="1">

                    <Setter Property="Background" Value="Write" />

                </Trigger>

            </Style.Triggers>

        </Style>

    </DataGrid.RowStyle>

</DataGrid>