Crossed cubes network is a kind of interconnection structure as a basis for distributed memory parallel computer architecture. Reliability takes an important role in fault tolerant computing on multiprocessor systems. Connectivity is a vital metric to explore fault tolerance and reliability of network structure based on a graph model. Let be a connected graph. The k-conditional edge connectivity is the cardinality of the minimum edge cuts , if any, whose deletion disconnects and each component of has property of minimum degree . The k-conditional connectivity can be defined similarly. In this paper, we determine the k- conditional (edge) connectivity of crossed cubes for small k. And we also prove other properties of .