We present team semantics for two of the most important linear and branching time specification languages, Linear Temporal Logic (LTL) and Computation Tree Logic (CTL). With team semantics, LTL is able to express hyperproperties, which have in the last decade been identified as a key concept in the verification of information flow properties. We study basic properties of the logic and classify the computational complexity of its satisfiability, path, and model checking problem. Further, we examine how extensions of the basic logic react to adding additional atomic operators. Finally, we compare its expressivity to the one of HyperLTL, another recently introduced logic for hyperproperties. Our results show that LTL with team semantics is a viable alternative to HyperLTL, which complements the expressivity of HyperLTL and has partially better algorithmic properties. For CTL with team semantics, we investigate the computational complexity of the satisfiability and model checking problem. The satisfiability problem is shown to be EXPTIME-complete while we show that model checking is PSPACE-complete.