Cervical cancer cells and HPV+ head and neck cancer cells express three testis-specific genes not normally expressed in somatic cells: testicular cell adhesion molecule 1 (TCAM1), synaptonemal complex protein 2 (SYCP2) and stromal antigen 3 (STAG3). Among the three markers, TCAM1 and SYCP2 are early detection markers. Various methods for identifying a human or non-human animal as a candidate for further examination for cervical cancer, preneoplastic lesion for cervical cancer, head and neck cancer, or preneoplastic lesion for head and neck cancer are disclosed. Methods of detecting said cancers and preneoplastic lesions, methods of screening for drugs for treating said cancers and preneoplastic lesions, methods for monitoring the effectiveness of a treatment for said cancers, and methods of treating said cancers are also disclosed. Further disclosed are kits that can be used to practice the above methods.