In the Internet of Things (IoT), resource-constrained things are connected to the unreliable and untrusted Internet via IPv6 and 6LoWPAN networks. Even when they are secured with encryption and authentication, these things are exposed both to wireless attacks from inside the 6LoWPAN network and from the Internet. Since these attacks may succeed, Intrusion Detection Systems (IDS) are necessary. Currently, there are no IDSs that meet the requirements of the IPv6-connected IoT since the available approaches are either customized for Wireless Sensor Networks (WSN) or for the conventional Internet. In this paper we design, implement, and evaluate a novel intrusion detection system for the IoT that we call SVELTE. In our implementation and evaluation we primarily target routing attacks such as spoofed or altered information, sinkhole, and selective-forwarding. However, our approach can be extended to detect other attacks. We implement SVELTE in the Contiki OS and thoroughly evaluate it. Our evaluation shows that in the simulated scenarios, SVELTE detects all malicious nodes that launch our implemented sinkhole and/or selective forwarding attacks. However, the true positive rate is not 100%, i.e., we have some false alarms during the detection of malicious nodes. Also, SVELTE's overhead is small enough to deploy it on constrained nodes with limited energy and memory capacity.