Non-standard Analysis

I've just digested a chunk of Alain Robert's book, using internal set theory (adding a "standard" axiom to ZFC), and while it strikes me as very elegant, it still seems to require very awkward logical reasoning to actually get anything done. Maybe that's just me.

I'm worried that every approach to infinitesimals (i.e. not using limits) just pushes the difficulties to new places. Isn't there an easy way? I hear a voice saying "there is no royal road" but I think there must be.