Just installed a new battery and alternator. Since than, the brake, battery and door lights will flash on and off. Just recently the check engine light came on again. Does anyone have an idea of what it may be??

What code is picked up on the CEL.

I haven't taken it to get the code checked. It just came on today. The car runs fine thou just the same three lights go off and on.

It might run perfectly well... but you NEED to have the codes checked... if you have either of the lights on... the red or the orange... there will be codes telling you what the ECU sees as a problem.

If the brake and battery lights flash, you probably have a charging system problem.

If the CEL is on, go to an Advance Auto or Autozone and have them scan it for codes.

It sounds like a problem with the alternator, which was likely a remanufactured product. It's scary how little is often done to "reman" alternators. Most remanufacturers get everything "clean and shinny," but they do not replace the bearings or brush/regulator assembly. Since I rebuild alternators, I suspect the problem is with the brushes that are worn down too far--this is often the case. When they are worn down too far, they bounce at high rpm. It wouldn't surprise me if multiple codes were thrown. It's not unusual for the dash to light up like a Christmas tree, when the alternator is bad. Bottom line: install a new genuine Honda alternator and your problem will be solved.

A quick check of the regulated battery voltage may reveal the problem. With the engine running, test for 14 to 15 volts across the battery terminals with a multi-meter.