The difference in price of futures with different deliveries

I know that the price of a future is slightly higher than its SPOT price, and it reaches the SPOT price at delivery date. This difference covers the swap rate too.

I do not understand why the future price of some commodities is increased by delivery date, and some decreased.

For example;
Corn (H15) 385
Corn (K15) 393

Wheat (H15) 510
Wheat (K15) 507

The other major factor that is taken into account, especially agricultural futures, is the out look for supply and demand and old crop vs new crop.

If there is an adequate to high supply of a commodity the future prices will be higher than the spot month because commercial will sell the closer month and buy the further out month (in the same crop year) until the price difference between the two months reflects the "cost to carry" the actual commodity for that period. That means that if it cost 20 cents per bushel per month to pay for storage, then the highest that the five month out futures contract minus the two month out futures contract would never go above 60 cents per bushel because if it did, it would PAY to take delivery of the two month out futures contract and redeliver it five months out. That gives you an idea of what the widest spread between the months should be. If there is a bumper crop it will come very close to that level.

Now if there is a shortage, there won't be the selling pressure from the producers, but the users will still need to make their purchases to fulfill their commitments. In this situation the nearby month can move to be higher than the further out months because of demand. The users do not or can not shut down their operations so they continue to buy and bid up the price. The producers do not have the supply to sell so the selling pressure is light.

Hopefully this helped to answer your question. If you have any further questions feel free to ask of PM me.

GREEN pips to you always.

Yep. What SmoothTrader said above, and I believe its the interest rates that play a role too, just like futures of other instruments/products. If the interest rates have increased by expiry, then that too might be the reason why the futures prices rose closer to expiry. The more expensive it is to hold stock into the future, the more the price of the futures will it be (because of interest cost added to the spot/market cost of commodities). Hope that helps!