ake a look at this other SO: How to implement custom JsonConverter in JSON.NET to deserialize a List of base class objects?.

I used this as the basis for my own solution to the same problem.

Starting off with the JsonCreationConverter<T> referenced in that SO (slightly modified to fix issues with serialization of types in responses):

public abstract class JsonCreationConverter<T> : JsonConverter
{
    /// <summary>
    /// this is very important, otherwise serialization breaks!
    /// </summary>
    public override bool CanWrite
    {
        get
        {
            return false;
        }
    }
    /// <summary>
    /// Create an instance of objectType, based properties in the JSON object
    /// </summary>
    /// <param name="objectType">type of object expected</param>
    /// <param name="jObject">contents of JSON object that will be
    /// deserialized</param>
    /// <returns></returns>
    protected abstract T Create(Type objectType, JObject jObject);

    public override bool CanConvert(Type objectType)
    {
        return typeof(T).IsAssignableFrom(objectType);
    }

    public override object ReadJson(JsonReader reader, Type objectType,
      object existingValue, JsonSerializer serializer)
    {
        if (reader.TokenType == JsonToken.Null)
            return null;
        // Load JObject from stream
        JObject jObject = JObject.Load(reader);

        // Create target object based on JObject
        T target = Create(objectType, jObject);

        // Populate the object properties
        serializer.Populate(jObject.CreateReader(), target);

        return target;
    }

    public override void WriteJson(JsonWriter writer, object value,
      JsonSerializer serializer)
    {
        throw new NotImplementedException();
    }
}
And now you can annotate your type with the JsonConverterAttribute, pointing Json.Net to a custom converter:

[JsonConverter(typeof(MyCustomConverter))]
public abstract class BaseClass{
  private class MyCustomConverter : JsonCreationConverter<BaseClass>
  {
     protected override BaseClass Create(Type objectType,
       Newtonsoft.Json.Linq.JObject jObject)
     {
       //TODO: read the raw JSON object through jObject to identify the type
       //e.g. here I'm reading a 'typename' property:

       if("DerivedType".Equals(jObject.Value<string>("typename")))
       {
         return new DerivedClass();
       }
       return new DefaultClass();

       //now the base class' code will populate the returned object.
     }
  }
}

public class DerivedClass : BaseClass {
  public string DerivedProperty { get; set; }
}

public class DefaultClass : BaseClass {
  public string DefaultProperty { get; set; }
}
Now you can use the base type as a parameter:

public Result Post(BaseClass arg) {

}
And if we were to post:

{ typename: 'DerivedType', DerivedProperty: 'hello' }
Then arg would be an instance of the DerivedClass, but if we posted:

{ DefaultProperty: 'world' }
Then you'd get an instance of the DefaultClass.