Playing my first game - question -- already out of logistic slots !!!!

Terran planets have a maximum of 24 logistics slots, asteroids 12, desert planets 36, volcanic and ice planets 20.

TEC can research a tech to increase the logistics capacity across the board for all planet types by I believe 4.

However, as labs take up 4 slots a piece, the answer to your question is effectively yes, this is normal.  You're going to need to spread out your labs amongst your worlds, if you want to build anything else at them.

Sole Soul is correct. But I dont understand why they never made the shipyards take up Military slots. What I would have done is make the shipyards take 10 military slots each. That way you could build more research/trade/broadcast/refinery at your home planet. Just my 2 cents.

Thnks for the info guys --- although at first it seems there should be at least a few more slots, I would imagine the devs thinking was that it would add to the strategy of the game as you have to really think of what you want to build before you make a decision.

Yep it's an important part of the strategy. If you build your military labs at a front line planet, and the enemy comes over to raze them, you no longer can build your best units.

You need to expand your empire to have more room for everything (planets tend to get filled with trade ports and culture centers too, at least with advent). On small maps it might be difficult to max out research trees or build big fleets, because of logistic slots not just the time span.

Which is why, when attacking an enemy, always prioritize planets above asteroids etc, for the logistics slots. Sometimes (esp. later stage game), you can even completely bypass an enemy asteroid for a planet. The loss of whatever things (labs, factories) in those logistics slots you razed from the planet are not easily replaced if the enemy does not have enough logistics slots elsewhere, and so, the effect on their ability to respond is quite significant for a long time.