PRESENT and MIBS are two lightweight block ciphers that are suitable for low resource devices such as radio-frequency identification tags. In this paper, we present the first biclique cryptanalysis of MIBS block cipher and a new biclique cryptanalysis of PRESENT block cipher. These attacks are performed on full-round MIBS-80 and full-round PRESENT-80. Using matching without matrix technique in the attack on MIBS and choosing a sub-key space of an internal round for key division eventuate to reduce the security of this cipher by 1 bit, while the data complexity of attack is 2 52 chosen plaintext. The attack on PRESENT-80 has a data complexity of at most 2 22 chosen plaintext and computational complexity of 2 79.34 encryption that both complexities are lower than of other cryptanalyses of full-round PRESENT-80 so far. Also, in this paper, we use early abort technique to efficiently filter out wrong keys in matching phase of biclique attack of PRESENT-80.