An extensive family of two-class PBIB designs is defined in Section 1 and given the title of NL designs. Several analogies of NL designs with Latin square type designs are discussed in Sections 1 and 2. Some of these designs have already appeared in scattered contexts. Section 3 gives a construction based on finite geometry for an infinite class of NL designs, and others can be constructed by methods to be taken up elsewhere. An extension to designs with more than two associate classes is indicated in Section 4.