For some absorbing chains the time to the absorption may be sufficiently long to allow a certain type of stationarity (called quasi-stationary) to set in transient states. In this paper we solve a problem related to quasi-stationary distributions of Markov chains. We consider absorbing chains with more than one absorbing states and study the different types of quasi-stationary distribution conditional on an eventual absorption into a specified state. We compare these with the unconditional quasi-stationary distributions when the absorbing subchain is regarded as a single absorbing state. The problem of quasi-stationarity have been motivated by some biological research.