You can define it as an application resource:
<Application x:Class="xxxxxx"
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
xmlns:clr="clr-namespace:System;assembly=mscorlib"
StartupUri="MainWindow.xaml">
<Application.Resources>
<clr:String x:Key="MyConstString">My string</clr:String>
</Application.Resources>
</Application>