In this paper we generalize some of the results from \cite{sdaWMV} 
to the noncommutative case. We present reversed left-pseudo-BCK(pP) 
algebras, reversed left-pseudo-BCK(pRP) algebras and  
left-X-pseudo-BCK(pR) algebras (i.e porims), left-X-pseudo-BCK(pRP) 
algebras. We prove they are  categorically  equivalent.