I had this exact same thing with DS when he was smaller. I had good results using a technique called "wake to sleep". It involves gently rousing (but not waking) about 5-10 mins before the expected waking time, the theory being that this would "reset" the sleep cycle. I used to gently stroke DS' hand until he moved a little bit and then would let him settle into a deeper sleep again. Took a little bit of practice to learn just how much to rouse him but it worked great for us. I found it on google
Try an earlier bedtime as sometimes a sign of being over tired. Or make sure they're winded - this used to wake up my dd up even up to 18 months. Another thing is to make sure they're not too hot or cold.