I honestly think both LTC and DOGE are way overstaying their welcome as I really can't see any reason whatsoever that would warrant their current price. I'm curious though, why people think otherwise.
They are the fairest, simplest and least controversial coins out there (besides BTC). Can you ask for more?
Of course there will always be some special ultra innovative coin right around the corner, whose complicated features may or may not work, whose launch may or may not be transparent, whose distribution may or may not be perceived as fair and whose construction as a whole may or may not be stable.
However, most people don't like uncertainty and any marginal benefit that innovative coins offer has not been great enough to make a significant impact.
Dogecoin, Litecoin and Bitcoin on the other hand all three are classical plain vanilla crypto currencies, who thrive on their network effects, have the basic crypto currency features and as a trinity offer at least some diversification within this field.