Click here to learn How to Install Tekkit.
The Out of Memory! crash can occur more frequently in Tekkit and the Technic Pack mod packs because of the increased amount of in-game processes that Minecraft has to keep track with. Running complex redstone machinery, Industrial Craft machines and Equivalent Exchange at the same time plays a major part in increasing the memory usage for Minecraft.
Saying that, some players actually report that they have increased performance when playing these mod packs. This is due to the inclusion of the Optifine mod, which have a post about here.
Allocating more memory to Minecraft is one of the best ways that you can fix the Minecraft Has Run Out of Memory error. With Tekkit and the Technic Pack being more memory intensive than vanilla Minecraft a great way to stop crashes is by opening up more memory for Minecraft to use. We have a great guide on how to do this.
Furthermore, installing 64-bit Java is a great way to ensure that Tekkit and Technic Pack are running on the best client they can. If you are using a 64-bit operating system then you should be running on a 64-bit version of Java, but many people are not. Check out our guide on how to tell if you need 64-bit Java and where you can get it.
For all of our other fixes that you can use to avoid the memory error then make sure to check out our Fixes page.