I Have 2 Lincoln Town Cars 1999 & 2003

Both of my town cars have the same problem. When 1st starting to drive and I get to around 30 mph and the car shifts into the next gear, both cars act like what I will call loaping or another way of stating it is they act like very short repeating hesitations. If the gas peddle is pushed down further so that the car speeds up faster, it doesn't do it. I have a friend that is an excellant Ford transmission man that was trained and worked at Ford for over 17 years. He says that it is not the transmission. Again, both cars are doing the same thing. We have even changed the fuel line filter with no success there. We also used the OBDII and no codes show up. At idle, the car runs very smooth. At speeds over 65 miles per hour and when accellerating hard, they both run good. When the problem occurs it acts like the motor is cutting out, sometimes just once and sometimes repetitively. The 1999 has 214,000 miles and the 2003 has 367,000 miles. We could sure use some help. Thanks