Tony Dale has written out his responses to someone asking about house church and the question of authority. You can read the entire text here if you wish. Here are some excerpts:
How do other house churches deal with the issue of being under authority?
[Tony] This varies widely between house churches. Most that we find ourselves associated with recognize who the people were who helped them come into being. As Paul stated to the Corinthians: "For even if you had ten thousand others to teach you about Christ, you have only one spiritual father. For I became your father in Christ Jesus when I preached the Good News to you. So I ask you to follow my example and do as I do" (1 Cor 4:15-16). Clearly Paul expected, like any parent, that his children would recognize him, not because of some office that he held, but because of the relationships that had been built.
Is authority that big of an issue (with denominations it certainly is)?
[Tony] Another great question. My answer would be a resounding, "No." It really is not a big issue. It is the natural outflow of relationship. If authority is not based on relationship, but on postition, then we have moved into that which Jesus forbid! See Matthew 20:24-27.
We believe in multiple leadership -- having at least two leaders for each house church... and we are considering setting up an advisory/accountability board. This would be a group of godly men we would be accountable to.
[Tony] I think that you are probably still thinking in rather traditional ways. Leadership in churches is always a plurality, but this is probably expressed best within a network of churches, say in a region or town. Most house churches are more like family. You know who the parents are in a family. You don't have to delegate this type of relationship. For example, in the network of home churches around here there is usually a couple or a couple of singles who will take responsibilty to help facilitate the group. But the authority here is not that of being the "leader" but rather of the parent who is helping by serving the group. Between the local network of house churches, the "leaders" or facilitators would together constitute a team leadership of the network. But even there we keep things very fluid, and encourage anyone that they are welcome to come to any of the "leadership" times that they want to come to. We also encourage input from outside from apostolic and prophetic folk (see Eph. 2:20) that we love and respect. But that does not give those people "authority over" us, but rather lets us draw on their wisdom and respond to their maturity.
(Just a wee side note: Tony will be one of the presenters at the California Regional House Church Conference in May--HouseChurchLife.com