Summary: Employing the common property (E.A), we prove some common fixed point theorems for weakly compatible mappings via an implicit relation in Menger PM spaces. Some results on similar lines satisfying quasicontraction conditions as well as

$\psi $-type contraction conditions are also proved in Menger PM spaces. Our results substantially improve the corresponding theorems contained in

*A. Branciari* [Int. J. Math. Math. Sci. 29, No. 9, 531–536 (2002;

Zbl 0993.54040)],

*B. E. Rhoades* [ibid. 2003, No. 63, 4007–4013 (2003;

Zbl 1052.47052)], and

*P. Vijayaraju, B. E. Rhoades* and

*R. Mohanraj* [ibid. 2005, No. 15, 2359–2364 (2005;

Zbl 1113.54027)] and also some others in Menger as well as metric spaces. Some related results are also derived besides furnishing illustrative examples.