Pseudorandom sequences are used in many areas of cryptography for instance as a key stream of stream ciphers. These sequences have to be unpredictable and resist to known attacks, hence they are supposed to satisfy some properties e.g., large linear complexity and low correlation. Since they are generated by a sequence generator, we also need to talk about a family of sequences and its properties. A family of sequences must have complex and rich structure e.g., large family size, large family complexity, strict avalanche property and low crosscorrelation. In this study, we present two large families of pseudorandom binary sequences with low cross-correlation measure. In fact, we extend the family construction method given by K. Gyarmati, C. Mauduit and A. Sarkozy and obtain larger families.