Based on your answers I solved the Problem like described below. I post it, because i guess that other beginners in WPF could find it useful.
I have singleton class (InfoPool.cs) wich implements INotifyChangedProperty. It's used to provide appwide bindable properties. This class is used by an ObjectDataProvider in App.xaml. So it's very "easy" to bind to a property 
InfoPool.cs (the Singleton code is from http://csharpindepth.com/Articles/General/Singleton.aspx 5th Version. I changed the Instance Property to GetInstance() Method, because the OPD needs an Method)
public sealed class InfoPool : INotifyPropertyChanged
{
    InfoPool()
    {
    }
    public static InfoPool GetInstance()
    {
        return Nested.instance;
    }
    class Nested
    {
        static Nested()
        {
        }
        internal static readonly InfoPool instance = new InfoPool();
    }
    public event PropertyChangedEventHandler PropertyChanged;
    public void OnPropertyChanged(PropertyChangedEventArgs e)
    {
        if (PropertyChanged != null)
        {
            PropertyChanged(this, e);
        }
    }
    private String strProp = "default String";
    private Double dblProp = 1.23456;
    public String StrProp
    {
        get { return strProp; }
        set 
        { 
            strProp = value;
            OnPropertyChanged(new PropertyChangedEventArgs("StrProp"));
        }
    }
    public Double DblProp
    {
        get { return dblProp; }
        set 
        { 
            dblProp = value;
            OnPropertyChanged(new PropertyChangedEventArgs("DblProp"));
        }
    }
The ObjectDataProvider in App.xaml
<Application.Resources>
    <ResourceDictionary>
        <ObjectDataProvider x:Key="OPDInfo" ObjectType="{x:Type local:InfoPool}" MethodName="GetInstance" d:IsDataSource="True"/>
    </ResourceDictionary>
</Application.Resources>
An here are 2 ways to bind to the OPD
<StackPanel>
    <TextBlock x:Name="tbprop1" Text="{Binding Path=StrProp, Source={StaticResource OPDInfo}}" />
    <TextBlock x:Name="tbprop2" Text="{Binding DblProp}" ToolTip="{Binding StrProp}" DataContext="{StaticResource OPDInfo}" />
</StackPanel>
That's it. Please comment, cause I'm new to this ;-)