Behavioural traits play an important role in invasion success, yet little is known about how species behave when they arrive in a new environment. In this study we examined the behaviour of the invasive shrimp Palaemon macrodactylus after entering in a novel place with a single refuge during a 24 h solitary phase, and after the introduction of a conspecific or heterospecific (the native goby Gobiosoma parri), in the next 24 h (competition phase), comparing their responses as residents and as intruders. Time spent swimming, using the shelter and the frequency of interactions (withdrawing touches) were quantified. Shrimps entering to a new empty environment, swam most of the time in the first hours, while the use of shelter increased steadily. The use of shelter in shrimps was affected by sex and residency status. Females won the shelter to males, while residents won the shelter to intruders. In the interspecific competition, refuge was always won by gobies and shrimps showed no resistance. Obtaining shelter was not generated through aggressive behaviours, but rather a hierarchy established through some other type of interactions. We propose that both prolonged swimming, which could indicate exploratory behaviour, and a social organization without aggressive confrontations could be key to the initiation of an invasion in this species.