C# - Creating Instances Of A Class Inside A Static PageMethod Thread Safe?

I am using jQuery to call PageMethods. For certain operations, the current user credentials must be validated and for other operations, I need to call other static methods. Here is some sample code:

Sample #1

[WebMethod]
public static void PostComment(string comment)
{
UserAuth auth = new UserAuth();
if (auth.isAuthenticated)
{
//Post comment here...
}
}

Sample #2

[WebMethod]
public static string GetComment(int commentId)
{
commentDto comment = //get comment data from the database...
string friendlyDate = ConvertFriendlyDate(comment.commentDate);
return friendlyDate + " " + comment.text;
}
public static string ConvertFriendlyDate(DateTime commentDate)
{
string friendlyDate = //call static utility method to convert date to friendly format
return friendlyDate;
}

Will I be safe using these kinds of operations? Am I better to drop page methods and just call a separate ASPX page for my AJAX requests?