Nowadays, we have four FHE cryptosystems, namely TFHE, BFV/BGV and CKKS, which are becoming a kind of standards for FHE use in practice. However, each of these schemes suffer from some kind of limitations of their own. Some allow for computations over large plaintexts, while some allow for unbounded number of operations. In some schemes bootstrapping is still impractical, while TFHE bootstrapping is quite efficient. In this thesis we wish to investigate an efficient switching mechanisms between different FHE cryptosystems. This would open up wide range of applications in deep Neural Networks evaluation over encrypted data using scheme switching.